on the finite element method for singularly perturbed reaction diffusion problems in two and one dimensions second order elliptic boundary value problems which are allowed to degenerate into zero order equations are considered the behavior of the ordinary galerkin finite element method without special arrangements to treat singularities is studied as the problem ranges from true second order to singularly perturbed

image analysis using hahn moments this paper shows how hahn moments provide a unified understanding of the recently introduced chebyshev and krawtchouk moments the two latter moments can be obtained as particular cases of hahn moments with the appropriate parameter settings and this fact implies that hahn moments encompass all their properties the aim of this paper is twofold 1 to show how hahn moments as a generalization of chebyshev and krawtchouk moments can be used for global and local feature extraction and 2 to show how hahn moments can be incorporated into the framework of normalized convolution to analyze local structures of irregularly sampled signals

a multi level stabilized finite element method for the stationary navier stokes equations abstract this paper proposes and analyzes a multi level stabilized finite element method for the two dimensional stationary navier stokes equations approximated by the lowest equal order finite element pairs the method combines the new stabilized finite element method with the multi level discretization under the assumption of the uniqueness condition the multi level stabilized finite element method consists of solving the nonlinear problem on the coarsest mesh and then performs one newton correction step on each subsequent mesh thus only solving one large linear systems the error analysis shows that the multi level stabilized finite element method provides an approximate solution with the convergence rate of the same order as the usual stabilized finite element solution solving the stationary navier stokes equations on a fine mesh for an appropriate choice of mesh widths h j h j 1 2 j 1 j moreover the numerical illustrations agree completely with the theoretical expectations therefore the multi level stabilized finite element method is more efficient than the standard one level stabilized finite element method

ultraconvergence of the patch recovery technique ii the ultraconvergence property of a gradient recovery technique proposed by zienkiewicz and zhu is analyzed for the laplace equation in the two dimensional setting under the assumption that the pollution effect is not present or is properly controlled it is shown that the convergence rate of the recovered gradient at an interior node is two orders higher than the optimal global convergence rate when even order finite element spaces and local uniform rectangular meshes are used

pseudotime method for shape design of euler flows we exploit a novel idea for the optimization of flows governed by the euler equations the algorithm consists of marching on the design hypersurface while improving the distance to the state and costate hypersurfaces we consider the problem of matching the pressure distribution to a desired one subject to the euler equations for both subsonic and supersonic flows we limited our investigation to two dimensional test cases the rate of convergence to the minimum for the cases considered is three to four times slower than that of the analysis problem results are given for ringleb flow and a shockless compression case

a new stabilized finite element method for the transient navier stokes equations abstract this paper is concerned with the development and analysis of a new stabilized finite element method based on two local gauss integrations for the two dimensional transient navier stokes equations by using the lowest equal order pair of finite elements this new stabilized finite element method has some prominent features parameter free avoiding higher order derivatives or edge based data structures and stabilization being completely local at the element level an optimal error estimate for approximate velocity and pressure is obtained by applying the technique of the galerkin finite element method under certain regularity assumptions on the solution compared with other stabilized methods using the same pair of mixed finite elements for the two dimensional transient navier stokes equations through a series of numerical experiments it is shown that this new stabilized method has better stability and accuracy results

a comment on translation and scale invariants of tchebichef moments by hongqing zhu pattern recognition 40 2007 25302542 it points out wrong claim made by hongqing zhu 2007 it corrects this error by developing and using charlier moment the proposed charlier moment is a novel category the aim of the present comment is to point out wrong claim made by hongqing zhu 2007 on the computation of scaling invariants of tchebichef moments we also proposed a novel discrete orthogonal moments namely charlier moments and demonstrate that the scaling invariants of the charlier moments can be computed by using the method mentioned in the article of hongqing zhu 2007 experimental results show that our inference is correct

image analysis by tchebichef moments this paper introduces a new set of orthogonal moment functions based on the discrete tchebichef polynomials the tchebichef moments can be effectively used as pattern features in the analysis of two dimensional images the implementation of the moments proposed in this paper does not involve any numerical approximation since the basis set is orthogonal in the discrete domain of the image coordinate space this property makes tchebichef moments superior to the conventional orthogonal moments such as legendre moments and zernike moments in terms of preserving the analytical properties needed to ensure information redundancy in a moment set the paper also details the various computational aspects of tchebichef moments and demonstrates their feature representation capability using the method of image reconstruction

image analysis by krawtchouk moments a new set of orthogonal moments based on the discrete classical krawtchouk polynomials is introduced the krawtchouk polynomials are scaled to ensure numerical stability thus creating a set of weighted krawtchouk polynomials the set of proposed krawtchouk moments is then derived from the weighted krawtchouk polynomials the orthogonality of the proposed moments ensures minimal information redundancy no numerical approximation is involved in deriving the moments since the weighted krawtchouk polynomials are discrete these properties make the krawtchouk moments well suited as pattern features in the analysis of two dimensional images it is shown that the krawtchouk moments can be employed to extract local features of an image unlike other orthogonal moments which generally capture the global features the computational aspects of the moments using the recursive and symmetry properties are discussed the theoretical framework is validated by an experiment on image reconstruction using krawtchouk moments and the results are compared to that of zernike pseudo zernike legendre and tchebyscheff moments krawtchouk moment invariants are constructed using a linear combination of geometric moment invariants an object recognition experiment shows krawtchouk moment invariants perform significantly better than hu s moment invariants in both noise free and noisy conditions

translation and scale invariants of tchebichef moments discrete orthogonal moments such as tchebichef moments have been successfully used in the field of image analysis however the invariance property of these moments has not been studied mainly due to the complexity of the problem conventionally the translation and scale invariant functions of tchebichef moments can be obtained either by normalizing the image or by expressing them as a linear combination of the corresponding invariants of geometric moments in this paper we present a new approach that is directly based on tchebichef polynomials to derive the translation and scale invariants of tchebichef moments both derived invariants are unchanged under image translation and scale transformation the performance of the proposed descriptors is evaluated using a set of binary characters examples of using the tchebichef moments invariants as pattern features for pattern classification are also provided

a contribution to the numerical prediction of unsteady flows methods based on flux differe nce splitting are investigated with reference to the prediction of unsteady compressible flows they combine the feature of taking into account the wake like nature of these flows and the capability of correctly capturing shock waves two recently proposed approaches and a third one suggested here are compared for one dimensional flow with particular reference to the means of operating the splitting they are extended to the cases of variable area ducts and a general transformation of the independent variables firstand second order accurate schemes are presented and procedures for the computation at the boundaries are shown finally numerical experiments are reported and discussed

superconvergence of finite element approximations for the stokes problem by projection methods this paper derives a general superconvergence result for finite element approximations of the stokes problem by using projection methods proposed and analyzed recently by wang j math study 33 2000 pp 229 243 for the standard galerkin method the superconvergence result is based on some regularity assumption for the stokes problem and is applicable to any finite element method with regular but nonuniform partitions the method is proved to give a convergent scheme for certain finite element spaces which fail to satisfy the well known uniform inf sup condition of brezzi and babuska

a stabilized finite element method based on two local gauss integrations for the stokes equations this paper considers a stabilized method based on the difference between a consistent and an under integrated mass matrix of the pressure for the stokes equations approximated by the lowest equal order finite element pairs i e the p 1 p 1 and q 1 q 1 pairs this method only offsets the discrete pressure space by the residual of the simple and symmetry term at element level in order to circumvent the inf sup condition optimal error estimates are obtained by applying the standard galerkin technique finally the numerical illustrations agree completely with the theoretical expectations

a local superconvergence analysis of the finite element method for the stokes equations by local projections abstract in this paper we focus on a local superconvergence analysis of the finite element method for the stokes equations by local projections the local and global superconvergence results of finite element solutions are provided for the stokes problem under some corresponding regularity assumptions conclusion can be drawn that the local superconvergence has advantages over the global superconvergence in two important aspects on the one hand it offsets theoretical limitation in practical applications on the other hand interior estimates are derived on the base of local properties of the domain without global smoothness for the exact solution and prior regularity of the problem globally over the whole domain

translation invariants of zernike moments moment functions defined using a polar coordinate representation of the image space such as radial moments and zernike moments are used in several recognition tasks requiring rotation invariance however this coordinate representation does not easily yield translation invariant functions which are also widely sought after in pattern recognition applications this paper presents a mathematical framework for the derivation of translation invariants of radial moments defined in polar form using a direct application of this framework translation invariant functions of zernike moments are derived algebraically from the corresponding central moments both derived functions are developed for non symmetrical as well as symmetrical images they mitigate the zero value obtained for odd order moments of the symmetrical images vision applications generally resort to image normalization to achieve translation invariance the proposed method eliminates this requirement by providing a translation invariance property in a zernike feature set the performance of the derived invariant sets is experimentally confirmed using a set of binary latin and english characters

the superconvergent patch recovery and a posteriori error estimates part 2 error estimates and adaptivity in this second part of the paper the issue of a posteriori error estimation is discussed in particular we derive a theorem showing the dependence of the effectivity index for the zienkiewicz zhu error estimator on the convergence rate of the recovered solution this shows that with superconvergent recovery the effectivity index tends asymptotically to unity the superconvergent recovery technique developed in the first part of the paper1 is the used in the computation of the zienkiewicz zhu error estimator to demonstrate accurate estimation of the exact error attainable numerical tests are shown for various element types illustrating the excellent effectivity of the error estimator in the energy norm and pointwise gradient stress error estimation several examples of the performance of the error estimator in adaptive mesh refinement are also presented

an interior estimate of superconvergence for finite element solutions for second order elliptic problems on quasi uniform meshes by local projections this paper establishes some superconvergence estimates for finite element solutions of second order elliptic problems by a projection method depending only on local properties of the domain and the finite element solution the projection method is a postprocessing procedure that constructs a new approximation by using the method of least squares in particular some local superconvergence estimates in the l2 and l infty norms are derived for the local projections of the galerkin finite element solution the results have two prominent features first they are established for any quasi uniform meshes which are of practicalimportance in scientific computation second they are derived on the basis of local properties of the domain and the solution for the second order elliptic problem therefore the result of this paper can be employed to provide useful a posteriori error estimators in practical computing

superconvergence of the velocity along the gauss lines in mixed finite element methods superconvergence for the velocity along the gauss lines is derived for the mixed finite element method for the second order elliptic equation in rectangular domains these estimates are based on the rectangular finite elements of raviart thomas type

superconvergence in finite element methods and meshes that are locally symmetric with respect to a point consider a second order elliptic boundary value problem in any number of space dimensions with locally smooth coefficients and solution consider also its numerical approximation by standard conforming finite element methods with for example fixed degree piecewise polynomials on a quasi uniform mesh family the h method it will be shown that if the finite element function spaces are locally symmetric about a point x 0 with respect to the antipodal map x to x 0 x x 0 then superconvergence ensues at xo under mild conditions on what happens outside a neighborhood of x 0 for piecewise polynomials of even degree superconvergence occurs in function values for piecewise polynomials of odd degree it occurs in derivatives