on the finite volume element method for general self adjoint elliptic problems the finite volume element method fve is a discretization technique for partial differential equations this paper develops discretization energy error estimates for general self adjoint elliptic boundary value problems with fve based on triangulations on which there exist linear finite element spaces and a very general type of control volumes covolumes the energy error estimates of this paper are also optimal but the restriction conditions for the covolumes given in r e bank and d j rose siam j numer anal 24 1987 pp 777 787 z q cai numer math 58 1991 pp 713 735 are removed the authors finally provide a counterexample to show that an expected l2 error estimate does not exist in the usual sense it is conjectured that the optimal order of u u h 0 omega should be o h for the general case

finite volume element methods for non definite problems the error estimates for finite volume element method applied to 2 and 3 d non definite problems are derived a simple upwind scheme is proven to be unconditionally stable and first order accurate

demosaicing with directional filtering and a posteriori decision most digital cameras use a color filter array to capture the colors of the scene downsampled versions of the red green and blue components are acquired and an interpolation of the three colors is necessary to reconstruct a full representation of the image this color interpolation is known as demosaicing the most effective demosaicing techniques proposed in the literature are based on directional filtering and a posteriori decision in this paper we present a novel approach to this reconstruction method a refining step is included to further improve the resulting reconstructed image the proposed approach requires a limited computational cost and gives good performance even when compared to more demanding techniques

explicit and averaging a posteriori error estimates for adaptive finite volume methods local mesh refining algorithms known from adaptive finite element methods are adopted for locally conservative and monotone finite volume discretizations of boundary value problems for steady state convection diffusion reaction equations the paper establishes residual type explicit error estimators and averaging techniques for a posteriori finite volume error control with and without upwind in global h1 and l2 norms reliability and efficiency are verified theoretically and confirmed empirically with experimental support for the superiority of the suggested adaptive mesh refining algorithms over uniform mesh refining a discussion of adaptive computations in the simulation of contaminant concentration in a nonhomogeneous water reservoir concludes the paper

a residual type a posteriori error estimate of finite volume element method for a quasi linear elliptic problem in this paper we analyze a residual type a posteriori error estimator of the finite volume element method for a quasi linear elliptic problem of nonmonotone type and derive computable upper and lower bounds on the error in the h 1 norm numerical experiments are provided to illustrate the performance of the proposed estimator

discontinuous galerkin methods for quasi linear elliptic problems of nonmonotone type in this paper both symmetric and nonsymmetric interior penalty discontinuous hp galerkin methods are applied to a class of quasi linear elliptic problems which are of nonmonotone type using brouwer s fixed point theorem it is shown that the discrete problem has a solution and then using lipschitz continuity of the discrete solution map uniqueness is also proved a priori error estimates in the broken h 1 norm which are optimal in h and suboptimal in p are derived moreover on a regular mesh an hp error estimate for the l 2 norm is also established finally numerical experiments illustrating the theoretical results are provided

off diagonal terms in symmetric operators in this paper we provide a quantitative comparison of two obstructions for a given symmetric operator s with dense domain in hilbert space h to be self adjoint the first one is the pair of deficiency spaces of von neumann and the second one is of more recent vintage let p be a projection in h we say that it is smooth relative to s if its range is contained in the domain of s we say that smooth projections pi i 1 diagonalize s if a i pi spi 0 for all i and b supi pi i if such projections exist then s has a self adjoint closure i e s has a spectral resolution and so our second obstruction to self adjointness is defined from smooth projections pi with i pi spi 0 we prove results both in the case of a single operator s and a system of operators

a two grid finite difference scheme for nonlinear parabolic equations we present a two level finite difference scheme for the approximation of nonlinear parabolic equations discrete inner products and the lowest order raviart thomas approximating space are used in the expanded mixed method in order to develop the finite difference scheme analysis of the scheme is given assuming an implicit time discretization in this two level scheme the full nonlinear problem is solved on a coarse grid of size h the nonlinearities are expanded about the coarse grid solution and an appropriate interpolation operator is used to provide values of the coarse grid solution on the fine grid in terms of superconvergent node points the resulting linear but nonsymmetric system is solved on a fine grid of size h some a priori error estimates are derived which show that the discrete l infty l2 and l2 h1 errors are o h 2 h 4 d 2 delta t where d geq 1 is the spatial dimension

two grid methods for finite volume element approximations of nonlinear parabolic equations two grid methods are studied for solving a two dimensional nonlinear parabolic equation using finite volume element method the methods are based on one coarse grid space and one fine grid space the nonsymmetric and nonlinear iterations are only executed on the coarse grid and the fine grid solution can be obtained in a single symmetric and linear step it is proved that the coarse grid can be much coarser than the fine grid the two grid methods achieve asymptotically optimal approximation as long as the mesh sizes satisfy h o h 3 lnh as a result solving such a large class of nonlinear parabolic equations will not be much more difficult than solving one single linearized equation

each averaging technique yields reliable a posteriori error control in fem on unstructured grids part ii higher order fem averaging techniques are popular tools in adaptive finite element methods since they provide efficient a posteriori error estimates by a simple postprocessing in the second paper of our analysis of their reliability we consider conforming h fem of higher i e not of lowest order in two or three space dimensions in this paper reliablility is shown for conforming higher order finite element methods in a model situation the laplace equation with mixed boundary conditions emphasis is on possibly unstructured grids nonsmoothness of exact solutions and a wide class of local averaging techniques theoretical and numerical evidence supports that the reliability is up to the smoothness of given right hand sides

a simple error estimator and adaptive procedure for practical engineerng analysis a new error estimator is presented which is not only reasonably accurate but whose evaluation is computationally so simple that it can be readily implemented in existing finite element codes the estimator allows the global energy norm error to be well estmated and alos gives a good evaluation of local errors it can thus be combined with a full adaptive process of refinement or more simply provide guidance for mesh redesign which allows the user to obtain a desired accuracy with one or two trials when combined with an automatic mesh generator a very efficient guidance process to analysis is avaiable estimates other than the energy norm have successfully been applied giving for instance a predetermined accuracy of stresses

a posteriori error estimates of two grid finite volume element methods for nonlinear elliptic problems abstract in this paper we study the a posteriori error estimates of two grid finite volume element method for second order nonlinear elliptic equations we derive the residual based a posteriori error estimator and prove the computable upper and lower bounds on the error in h 1 norm the a posteriori error estimator can be used to assess the accuracy of the two grid finite volume element solutions in practical applications numerical examples are provided to illustrate the performance of the proposed estimator

analysis of a finite volume element method for the stokes problem in this paper we propose a stabilized conforming finite volume element method for the stokes equations on stating the convergence of the method optimal a priori error estimates in different norms are obtained by establishing the adequate connection between the finite volume and stabilized finite element formulations a superconvergence result is also derived by using a postprocessing projection method in particular the stabilization of the continuous lowest equal order pair finite volume element discretization is achieved by enriching the velocity space with local functions that do not necessarily vanish on the element boundaries finally some numerical experiments that confirm the predicted behavior of the method are provided

color demosaicking via directional linear minimum mean square error estimation digital cameras sample scenes using a color filter array of mosaic pattern e g the bayer pattern the demosaicking of the color samples is critical to the image quality this paper presents a new color demosaicking technique of optimal directional filtering of the green red and green blue difference signals under the assumption that the primary difference signals pds between the green and red blue channels are low pass the missing green samples are adaptively estimated in both horizontal and vertical directions by the linear minimum mean square error estimation lmmse technique these directional estimates are then optimally fused to further improve the green estimates finally guided by the demosaicked full resolution green channel the other two color channels are reconstructed from the lmmse filtered and fused pds the experimental results show that the presented color demosaicking technique outperforms the existing methods both in psnr measure and visual perception

locally adapted tetrahedral meshes using bisection we present an algorithm for the construction of locally adapted conformal tetrahedral meshes the algorithm is based on bisection of tetrahedra a new data structure is introduced which simplifies both the selection of the refinement edge of a tetrahedron and the recursive refinement to conformity of a mesh once some tetrahedra have been bisected we prove that repeated application of the algorithm leads to only finitely many tetrahedral shapes up to similarity and we bound the amount of additional refinement that is needed to achieve conformity numerical examples of the effectiveness of the algorithm are presented

color image demosaicing using iterative residual interpolation a recently developed demosaicing methodology called residual interpolation ri has demonstrated superior performance over the conventional color component difference interpolation however it has been observed that the existing ri based methods fail to fully exploit the potential of ri strategy on the reconstruction of the most important g channel as only the r and b channels are restored through the ri strategy since any reconstruction error introduced in the g channel will be carried over into the demosaicing process of the other two channels this makes the restoration of the g channel highly instrumental to the quality of the final demosaiced image in this paper a novel iterative ri iri process is developed for reconstructing a highly accurate g channel first in essence it can be viewed as an iterative refinement process for the estimation of those missing pixel values on the g channel the key novelty of the proposed iri process is that all the three channels will mutually guide each other until a stopping criterion is met based on the restored g channel the mosaiced r and b channels will be respectively reconstructed by exploiting the existing ri method without iteration extensive simulations conducted on two commonly used test datasets for demosaicing algorithms have demonstrated that our algorithm has achieved the best performance in most cases compared with the existing state of the art demosaicing methods on both objective and subjective performance evaluations

multigrid algorithms for a vertex centered covolume method for elliptic problems we analyze v cycle multigrid algorithms for a class of perturbed problems whose perturbation in the bilinear form preserves the convergence properties of the multigrid algorithm of the original problem as an application we study the convergence of multigrid algorithms for a covolume method or a vertex centered finite volume element method for variable coefficient elliptic problems on polygonal domains as in standard finite element methods the v cycle algorithm with one pre smoothing converges with a rate independent of the number of levels various types of smoothers including point or line jacobi and gauss seidel relaxation are considered

some errors estimates for the box method we define and analyze several variants of the box method for discretizing elliptic boundary value problems in the plane our estimates show the error to be comparable to a standard galerkin finite element method using piecewise linear polynomials

some optimal error estimates for piecewise linear finite element approximations it is shown that the ritz projection onto spaces of piecewise linear finite elements is bounded in the sobolev space wl for 2 p oc this implies that for functions in wf n w2 the error in approximation behaves like 0 h in wp for 2 p oo and like 0 h2 in lp for 2 p oo in all these cases the additional logarithmic factor previously included in error estimates for linear finite elements does not occur

estimations a posteriori d un schema de volumes finis pour un probleme non lineaire resumedans cet article nous developpons des estimations a posteriori de l erreur commise en approchant un probleme elliptique non lineaire par une methode de volumes finis mvf de type vertex centered les estimateurs obtenus mesurent le residu de l equation forte et l irregularite de la solution discrete qui se traduit par des sauts a travers les inter elelments une condition sur la fonction flux numerique sera imposee pour traiter la non conformite du probleme au cours de l evaluation de l estimation summary we derive a posteriori error estimates for vertex centered finite volume discretizations of a class of non linear elliptic pdes the error estimates are of residual type and incorporate residuals of the pde in its strong form on the control volumes and jumps of the pde s prinicipal part across the element boundaries the non conformity of the discretization is taken into account by a condition on the numerical flux function

fully reliable localized error control in the fem if the first task in numerical analysis is the calculation of an approximate solution the second is to provide a guaranteed error bound and is often of equal importance the standard approaches in the a posteriori error analysis of finite element methods suppose that the exact solution has a certain regularity or the numerical scheme enjoys some saturation property for coarse meshes those asymptotic arguments are difficult to recast into rigorous error bounds the aim of this paper is to provide reliable computable error bounds which are efficient and complete in the sense that constants are estimated as well the main argument is a localization via a partition of unity which leads to problems on small domains two fully reliable estimates are established the sharper one solves an analytical interface problem with residuals following babuska and rheinboldt siam j numer anal 15 1978 pp 736 754 the second estimate is a modification of the standard residual based a posteriori estimate with explicit constants from local analytical eigenvalue problems for some class of triangulations we show that the efficiency constant is smaller than 2 5 according to our numerical experience the overestimation of our computable estimates proved to be reasonably small with an overestimation by a factor between 2 5 and 4 only

a posteriori error control in low order finite element discretisations of incompressible stationary flow problems computable a posteriori error bounds and related adaptive meshrefining algorithms are provided for the numerical treatment of monotone stationary flow problems with a quite general class of conforming and non conforming finite element methods a refined residual based error estimate generalises the works of verfurth dari duran and padra bao and barrett as a consequence reliable and efficient averaging estimates can be established on unstructured grids the symmetric formulation of the incompressible flow problem models certain nonnewtonian flow problems and the stokes problem with mixed boundary conditions a helmholtz decomposition avoids any regularity or saturation assumption in the mathematical error analysis numerical experiments for the partly nonconforming method analysed by kouhia and stenberg indicate efficiency of related adaptive mesh refining algorithms

color filter array demosaicking using high order interpolation techniques with a weighted median filter for sharp color edge preservation demosaicking is an estimation process to determine missing color values when a single sensor digital camera is used for color image capture in this paper we propose a number of new methods based on the application of taylor series and cubic spline interpolation for color filter array demosaicking to avoid the blurring of an edge interpolants are first estimated in four opposite directions so that no interpolation is carried out across an edge a weighted median filter whose filter coefficients are determined by a classifier based on an edge orientation map is then used to produce an output from the four interpolants to preserve edges using the proposed methods the original color can be faithfully reproduced with minimal amount of color artifacts even at edges

adaptive multispectral demosaicking based on frequency domain analysis of spectral correlation color filter array cfa interpolation or three band demosaicking is a process of interpolating the missing color samples in each band to reconstruct a full color image in this paper we are concerned with the challenging problem of multispectral demosaicking where each band is significantly undersampled due to the increment in the number of bands specifically we demonstrate a frequency domain analysis of the subsampled color difference signal and observe that the conventional assumption of highly correlated spectral bands for estimating undersampled components is not precise instead such a spectral correlation assumption is image dependent and rests on the aliasing interferences among the various color difference spectra to address this problem we propose an adaptive spectral correlation based demosaicking ascd algorithm that uses a novel anti aliasing filter to suppress these interferences and we then integrate it with an intra prediction scheme to generate a more accurate prediction for the reconstructed image our ascd is computationally very simple and exploits the spectral correlation property much more effectively than the existing algorithms experimental results conducted on two data sets for multispectral demosaicking and one data set for cfa demosaicking demonstrate that the proposed ascd outperforms the state of the art algorithms

on the finite volume element method the finite volume element method fve is a discretization technique for partial differential equations it uses a volume integral formulation of the problem with a finite partitioning set of volumes to discretize the equations then restricts the admissible functions to a finite element space to discretize the solution this paper develops discretization error estimates for general selfadjoint elliptic boundary value problems with fve based on triangulations with linear finite element spaces and a general type of control volume we establisho h estimates of the error in a discreteh 1 semi norm under an additional assumption of local uniformity of the triangulation the estimate is improved too h 2 results on the effects of numerical integration are also included

on q analogues of the fourier and hankel transforms for h exton s q analogue of the bessel function going back to w hahn in a special case but different from f h jackson s q bessel functions we derive hansen lommel type orthogonality relations which by a symmetry turn out to be equivalent to orthogonality relations which are q analogues of the hankel integral transform pair these results are implicit in the context of quantum groups in a paper by vaksman and korogodskii as a specialization we get q cosines and q sines which admit q analogues of the fourier cosine and fourier sine transforms

robust color demosaicking with adaptation to varying spectral correlations almost all existing color demosaicking algorithms for digital cameras are designed on the assumption of high correlation between red green blue or some other primary color bands they exploit spectral correlations between the primary color bands to interpolate the missing color samples but in areas of no or weak spectral correlations these algorithms are prone to large interpolation errors such demosaicking errors are visually objectionable because they tend to correlate with object boundaries and edges this paper proposes a remedy to the above problem that has long been overlooked in the literature the main contribution of this work is a hybrid demosaicking approach that supplements an existing color demosaicking algorithm by combining its results with those of adaptive intraband interpolation this is formulated as an optimal data fusion problem and two solutions are proposed one is based on linear minimum mean square estimation and the other based on support vector regression experimental results demonstrate that the new hybrid approach is more robust and eliminates the worst type of color artifacts of existing color demosaicking methods

compressive framework for demosaicing of natural images typical consumer digital cameras sense only one out of three color components per image pixel the problem of demosaicing deals with interpolating those missing color components in this paper we present compressive demosaicing cd a framework for demosaicing natural images based on the theory of compressed sensing cs given sensed samples of an image cd employs a cs solver to find the sparse representation of that image under a fixed sparsifying dictionary as opposed to state of the art cs based demosaicing approaches we consider a clear distinction between the interchannel color and interpixel correlations of natural images utilizing some well known facts about the human visual system those two types of correlations are utilized in a nonseparable format to construct the sparsifying transform our simulation results verify that cd performs better both visually and in terms of psnr than leading demosaicing approaches when applied to the majority of standard test images

the semidiscrete finite volume element method for nonlinear convection diffusion problem abstract in this work a semidiscrete finite volume element method for the nonlinear convection diffusion problem is considered under some regular assumptions we obtain the l2 and h1 norm error estimates of numerical solution furthermore we investigate two grid finite volume element method for the considered equations compared with the standard method the two grid method is of the same order as the standard method in the h1 norm as long as the mesh sizes satisfy h o h 1 3 however the two grid method involves much less work than the standard method finally some numerical results are provided to verify the established theoretical analysis

demosaicing by successive approximation in this paper we present a fast and high performance algorithm for color filter array cfa demosaicing cfa demosaicing is formulated as a problem of reconstructing correlated signals from their downsampled versions with an opposite phase the major contributions of this work include 1 a new iterative demosaicing algorithm in the color difference domain and 2 a spatially adaptive stopping criterion for suppressing color misregistration and zipper artifacts in the demosaiced images we have compared the proposed demosaicing algorithm with two current state of the art techniques reported in the literature ours outperforms both of them on demosaicing performance and computational cost

adaptive homogeneity directed demosaicing algorithm a cost effective digital camera uses a single image sensor applying alternating patterns of red green and blue color filters to each pixel location a way to reconstruct a full three color representation of color images by estimating the missing pixel components in each color plane is called a demosaicing algorithm this paper presents three inherent problems often associated with demosaicing algorithms that incorporate two dimensional 2 d directional interpolation misguidance color artifacts interpolation color artifacts and aliasing the level of misguidance color artifacts present in two images can be compared using metric neighborhood modeling the proposed demosaicing algorithm estimates missing pixels by interpolating in the direction with fewer color artifacts the aliasing problem is addressed by applying filterbank techniques to 2 d directional interpolation the interpolation artifacts are reduced using a nonlinear iterative procedure experimental results using digital images confirm the effectiveness of this approach

mixed finite element methods for quasilinear second order elliptic problems a mixed finite element method is developed to approximate the solution of a quasilinear second order elliptic partial differential equation the existence and uniqueness of the approximation are demonstrated and optimal rate error estimates are derived

a posteriori error estimation for the discrete duality finite volume discretization of the laplace equation an efficient and fully computable a posteriori error bound is derived for the discrete duality finite volume discretization of the laplace equation on very general two dimensional meshes the main ingredients are the equivalence of this method with a finite element like scheme and tools from the finite element framework numerical tests are performed with a stiff solution on highly nonconforming locally refined meshes and with a singular solution on triangular meshes

primary consistent soft decision color demosaicking for digital cameras patent pending color mosaic sampling schemes are widely used in digital cameras given the resolution of ccd sensor arrays the image quality of digital cameras using mosaic sampling largely depends on the performance of the color demosaicking process a common problem with existing color demosaicking algorithms is an inconsistency of sample interpolations in different primary color channels which is the cause of the most objectionable color artifacts to cure the problem we propose a new primary consistent soft decision framework pcsd of color demosaicking in the pcsd framework we make multiple estimates of a missing color sample under different hypotheses on edge or texture directions the estimates are made via a primary consistent interpolation meaning that all three primary components of a color are interpolated in the same direction the final estimate of a color sample is obtained by testing different interpolation hypotheses in the reconstructed full resolution color image and selecting the best via an optimal statistical decision or inference process a concrete color demosaicking method of the pcsd framework is presented this new method eliminates certain types of color artifacts of existing color demosaicking methods extensive experimental results demonstrate that the pcsd approach can significantly improve the image quality of digital cameras in both subjective and objective measures in some instances our gain over the competing methods can be as much as 7db

sparse representation for color image restoration sparse representations of signals have drawn considerable interest in recent years the assumption that natural signals such as images admit a sparse decomposition over a redundant dictionary leads to efficient algorithms for handling such sources of data in particular the design of well adapted dictionaries for images has been a major challenge the k svd has been recently proposed for this task and shown to perform very well for various grayscale image processing tasks in this paper we address the problem of learning dictionaries for color images and extend the k svd based grayscale image denoising algorithm that appears in this work puts forward ways for handling nonhomogeneous noise and missing information paving the way to state of the art results in applications such as color image denoising demosaicing and inpainting as demonstrated in this paper

two grid finite element method and its a posteriori error estimates for a nonmonotone quasilinear elliptic problem under minimal regularity of data abstract in this paper we propose and analyze a two grid finite element method for a class of quasilinear elliptic problems under minimal regularity of data in a bounded convex polygonal r 2 which can be thought of as a type of linearization of the nonlinear system using a solution from a coarse finite element space with this technique solving a quasilinear elliptic problem on the fine finite element space is reduced into solving a linear problem on the fine finite element space and solving the quasilinear elliptic problem on a coarse space convergence estimates in the h 1 norm are derived to justify the efficiency of the proposed two grid algorithm moreover we propose a natural and computationally efficient residual based a posteriori error estimator of the two grid finite element method for this nonmonotone quasilinear elliptic problem and derive the global upper and lower bounds on the error in the h 1 norm numerical experiments are provided to confirm our theoretical findings

on the accuracy of the finite volume element method for diffusion equations on composite grids this paper develops the finite volume element fve method which is similar to the so called control volume finite element method but tailored to composite grid applications fve is described for the general two dimensional diffusion equation in divergence form o h 3 2 discretization error estimates are then developed for the case of triangular elements these results are improved to o h 2 using a special modification involving rectilinear elements at the grid interface

multiscale finite element for problems with highly oscillatory coefficients in this paper we study a multiscale finite element method for solving a class of elliptic problems with finite number of well separated scales the method is designed to efficiently capture the large scale behavior of the solution without resolving all small scale features this is accomplished by constructing the multiscale finite element base functions that are adaptive to the local property of the differential operator the construction of the base functions is fully decoupled from element to element thus the method is perfectly parallel and is naturally adapted to massively parallel computers we present the convergence analysis of the method along with the results of our numerical experiments some generalizations of the multiscale finite element method are also discussed

a posteriori error estimates for finite volume method based on bilinear trial functions for the elliptic equation this paper is concerned with a residual type a posteriori error estimators for a finite volume method for the second order elliptic equation bilinear functions are used as trial functions in this finite volume method reliability and efficiency bounds for the error estimator are established numerical examples are provided to confirm the theory

error estimates in l 2 h 1 and l in covolume methods for elliptic and parabolic p roblems a unified approach in this paper we consider covolume or finite volume element methods for variable coefficient elliptic and parabolic problems on convex smooth domains in the plane we introduce a general approach for connecting these methods with finite element method analysis this unified approach is used to prove known convergence results in the h 1 l 2 norms and new results in the max norm for the elliptic problems we demonstrate that the error u u h between the exact solution u and the approximate solution u h in the maximum norm is o h 2 ln h in the linear element case furthermore the maximur norm error in the gradient is shown to be of first order similar results hold for the parabolic problems

on the accuracy of the finite volume element method based on piecewise linear polynomials we present a general error estimation framework for a finite volume element fve method based on linear polynomials for solving second order elliptic boundary value problems this framework treats the fve method as a perturbation of the galerkin finite element method and reveals that regularities in both the exact solution and the source term can affect the accuracy of fve methods in particular the error estimates and counterexamples in this paper will confirm that the fve method cannot have the standard o h2 convergence rate in the l2 norm when the source term has the minimum regularity only being in l2 even if the exact solution is in h2

global superconvergence and a posteriori error estimators of the finite element method for a quasi linear elliptic boundary value problem of nonmonotone type in this paper we are concerned with finite element approximations to a nonlinear elliptic partial differential equation with homogeneous dirichlet boundary conditions this kind of problems arises for example from modeling a stationary heat conduction in nonlinear inhomogeneous and anisotropic media for finite elements of degree k geq 1 in each variable by means of an interpolation postprocessing technique we obtain the global superconvergence of o hk 1 in the h1 norm and o hk 2 in the l2 norm provided the weak solution is sufficiently smooth as by products the global superconvergence results can be used to generate efficient a posteriori error estimators representative numerical examples are also given to illustrate our theoretical analysis

on galerkin approximations of a quasilinear nonpotential elliptic problem of a nonmonotone type abstract we prove the convergence of galerkin approximations for a second order quasilinear elliptic problem of a divergence form with nonlinear mixed boundary conditions the existence and uniqueness of a weak and approximate solution is studied as well

analysis of two grid methods for reaction diffusion equations by expanded mixed finite element methods we present two efficient methods of two grid scheme for the approximation of two dimensional semi linear reaction diffusion equations using an expanded mixed finite element method to linearize the discretized equations we use two newton iterations on the fine grid in our methods firstly we solve an original non linear problem on the coarse grid then we use twice newton iterations on the fine grid in our first method and while in second method we make a correction on the coarse grid between two newton iterations on the fine grid these two grid ideas are from xu s work siam j sci comput 1994 15 231 237 siam j numer anal 1996 33 1759 1777 on standard finite element method we extend the ideas to the mixed finite element method moreover we obtain the error estimates for two algorithms of two grid method it is showed that coarse space can be extremely coarse and we achieve asymptotically optimal approximation as long as the mesh sizes satisfy h h in the first algorithm and h h in second algorithm copyright 2006 john wiley sons ltd

guided image filtering in this paper we propose a novel explicit image filter called guided filter derived from a local linear model the guided filter computes the filtering output by considering the content of a guidance image which can be the input image itself or another different image the guided filter can be used as an edge preserving smoothing operator like the popular bilateral filter 1 but it has better behaviors near edges the guided filter is also a more generic concept beyond smoothing it can transfer the structures of the guidance image to the filtering output enabling new filtering applications like dehazing and guided feathering moreover the guided filter naturally has a fast and nonapproximate linear time algorithm regardless of the kernel size and the intensity range currently it is one of the fastest edge preserving filters experiments show that the guided filter is both effective and efficient in a great variety of computer vision and computer graphics applications including edge aware smoothing detail enhancement hdr compression image matting feathering dehazing joint upsampling etc

a posteriori error estimates based on hierarchical bases the authors present an analysis of an a posteriors error estimator based on the use of hierarchical basis functions the authors analyze nonlinear nonselfadjoint and indefinite problems as well as the selfadjoint positive definite case because both the analysis and the estimator itself are quite simple it is easy to see how various approximations affect the quality of the estimator as examples the authors apply the theory to some scalar elliptic equations and the stokes system of equations

two grid finite volume element method for linear and nonlinear elliptic problems two grid finite volume element discretization techniques based on two linear conforming finite element spaces on one coarse and one fine grid are presented for the two dimensional second order non selfadjoint and indefinite linear elliptic problems and the two dimensional second order nonlinear elliptic problems with the proposed techniques solving the non selfadjoint and indefinite elliptic problem on the fine space is reduced into solving a symmetric and positive definite elliptic problem on the fine space and solving the non selfadjoint and indefinite elliptic problem on a much smaller space solving a nonlinear elliptic problem on the fine space is reduced into solving a linear problem on the fine space and solving the nonlinear elliptic problem on a much smaller space convergence estimates are derived to justify the efficiency of the proposed two grid algorithms a set of numerical examples are presented to confirm the estimates

operator representations of a q deformed heisenberg algebra a class of well behaved representations of a q deformed heisenberg algebra previously introduced phys lett b 291 273 1992 z phys c 64 335 1994 is studied and classified

a novel two grid method for semilinear elliptic equations a new finite element discretization technique based on two coarse and fine subspaces is presented for a semilinear elliptic boundary value problem the solution of a nonlinear system on the fine space is reduced to the solution of two small one linear and one nonlinear systems on the coarse space and a linear system on the fine space it is shown both theoretically and numerically that the coarse space can be extremely coarse and still achieve asymptotically optimal approximation as a result the numerical solution of such a nonlinear equation is not significantly more expensive than the solution of one single linearized equation

global superconvergence and a posteriori error estimates of the finite element method for second order quasilinear elliptic problems in this paper we are concerned with the linear finite element approximations to the second order quasi linear elliptic problems by means of an interpolation postprocessing technique we develop the global superconvergence estimates in the h 1 and w 1 norms provided the weak solutions are sufficiently smooth based on the global superconvergent approximations we introduce and analyze the efficient postprocessing based a posteriori error estimators measured by the h 1 and w 1 norms respectively these can be used to assess the accuracy of the finite element solutions in applications numerical experiments are given to illustrate the global superconvergence estimates and the performance of the proposed estimators

each averaging technique yields reliable a posteriori error control in fem on unstructured grids part i low order conforming nonconforming and mixed fem averaging techniques are popular tools in adaptive finite element methods for the numerical treatment of second order partial differential equations since they provide efficient a posteriori error estimates by a simple postprocessing in this paper their reliablility is shown for conforming nonconforming and mixed low order finite element methods in a model situation the laplace equation with mixed boundary conditions emphasis is on possibly unstructured grids nonsmoothness of exact solutions and a wide class of averaging techniques theoretical and numerical evidence supports that the reliability is up to the smoothness of given right hand sides

multiscale gradients based color filter array interpolation single sensor digital cameras use color filter arrays to capture a subset of the color data at each pixel coordinate demosaicing or color filter array cfa interpolation is the process of estimating the missing color samples to reconstruct a full color image in this paper we propose a demosaicing method that uses multiscale color gradients to adaptively combine color difference estimates from different directions the proposed solution does not require any thresholds since it does not make any hard decisions and it is noniterative although most suitable for the bayer cfa pattern the method can be extended to other mosaic patterns to demonstrate this we describe its application to the lukac cfa pattern experimental results show that it outperforms other available demosaicing methods by a clear margin in terms of cpsnr and s cielab measures for both mosaic patterns

an adaptive finite element method for linear elliptic problems on propose une methode adaptative d elements finis basee sur une estimation d erreur optimale de norme maxima pour les problemes elliptiques lineaires

edge strength filter based color filter array interpolation for economic reasons most digital cameras use color filter arrays instead of beam splitters to capture image data as a result of this only one of the required three color samples becomes available at each pixel location and the other two need to be interpolated this process is called color filter array cfa interpolation or demosaicing many demosaicing algorithms have been introduced over the years to improve subjective and objective interpolation quality we propose an orientation free edge strength filter and apply it to the demosaicing problem edge strength filter output is utilized both to improve the initial green channel interpolation and to apply the constant color difference rule adaptively this simple edge directed method yields visually pleasing results with high cpsnr

a posteriori error estimation and adaptive mesh refinement techniques abstract we analyse three different a posteriori error estimators for elliptic partial differential equations they are based on the evaluation of local residuals with respect to the strong form of the differential equation on the solution of local problems with neumann boundary conditions and on the solution of local problems with dirichlet boundary conditions we prove that all three are equivalent and yield global upper and local lower bounds for the true error thus adaptive mesh refinement techniques based on these estimators are capable to detect local singularities of the solution and to appropriately refine the grid near these singularities some numerical examples prove the efficiency of the error estimators and the mesh refinement techniques