on the asymptotic behavior for a certain nonlinear evolution equation let x be a real banach space we shall say that an operator a with domain d a and range r a in x is accretive if lx x2 11 0 and yi e axi i 1 2 and that a satisfies the range condition if r z i 1 d a the closure of d a for all a 0 where 1 denotes the identity let g 0 co 0 co be a nonincreasing continuous function such that lim r13 g t 0 let x e x and consider the following initial value problem

a reconstruction based chebyshev collocation method for the poisson equation an accurate treatment of the gibbs wilbraham phenomenon on irregular interfaces abstract an accurate numerical solution of the laplace equation and poisson equation is desirable in physical problems related to fluid flows and spectral methods are well suited towards this goal however in the presence of an interface the solution is discontinuous owing to the interface jump conditions and thus the numerical approximation is susceptible to the gibbs wilbraham phenomenon leading to a reduced solution accuracy in order to resolve the discontinuity at the interface we propose a reconstruction technique wherein the approximate solution is expressed as the sum of an infinitely differentiable smooth function and a modified heaviside function the smooth function is composed of chebyshev polynomials while the modified heaviside function is expressed in a weak form using the jump conditions across the interface the reconstruction framework allows us to impose the interfacial conditions exactly to motivate further application of the technique we first present the underlying rationale by revisiting the work of wilbraham 1848 13 followed by the numerical implementation we present numerical solution of four equations to illustrate the application of the proposed technique i an ordinary differential equation ode ii the euler bernoulli equation iii the laplace equation and iv the poisson equation the laplace and poisson equation are solved on a square domain embedded with complex interfacial geometries in two dimensions and on a cube with a spherical interface in three dimensions the method achieves error in the maximum norm o 10 14 using approximately 30 modes in each direction and requires a computational time of less than a second for all the problems we also conduct a sensitivity analysis to demonstrate the robustness of the algorithm under sub grid scale perturbations to interface location an alternate derivation for the modified heaviside function is proposed that is distinct from the taylor series expansion used to treat interface conditions in difference methods the pointwise error plots are subsequently presented to demonstrate that the gibbs wilbraham phenomenon is accurately resolved finally we present concluding thoughts on the potential applications of the reconstruction technique

unbounded behavior and convergence of solutions of nonlinear volterra equations in banach spaces soit x un espace de banach reel de norme et a un operateur m accretif dans x on etudie le comportement asymptotique des solutions de l equation de volterra non lineaire g t u t b au t t r 0 ou b r r g r x sont donnees et est la convolution

grid generation techniques in computational fluid dynamics revue des differentes methodes on montre que les regions tridimensionnelles sont mieux traitees par fragmentation du champ en sous regions avec generation de grilles dans chaque sous region interet des grilles adaptatives couplees a des solutions physiques

a variational approach to optimal meshes a variational approach for the optimization of triangular or tetrahedral meshes is presented starting from some very basic assumptions we will rigorously demonstrate that the functional controlling optimality is of a certain type related to energy functionals in non linear elasticity it will be proved that these functionals attain their minima over admissible sets of mesh deformations which respect boundary conditions in addition the injectivity of the deformed mesh is discussed thereby it is possible to construct suitable meshes for various numerical applications

a comparison of numerical algorithms for fourier extension of the first second and third kinds the range of fourier methods can be significantly increased by extending a nonperiodic function f x to a periodic function f on a larger interval when f x is analytically known on the extended interval the extension is straightforward when f x is unknown outside the physical interval there is no standard recipe worse still like a radarless aircraft groping through fog the algorithm may wreck on the mountain in fog problem a function f x which is perfectly well behaved on the physical interval may very well have singularities in the extended domain in this article we compare several algorithms for successfully extending a function f x into the fog even when the analytic extension is singular the best third kind extension requires singular value decomposition with iterative refinement but achieves accuracy close to machine precision

asymptotic behavior of solutions to nonlinear volterra integral equations in section 2 we establish the existence of solutions to 1 1 and to related equations theorems 2 1 and 2 3 in contrast with previous papers e g 7 we do not assume that a is m accretive instead we require a to satisfy a weaker cone condition certain other facts are also included in this section throughout this paper we also assume that b is completely positive 6 in the third section we present two mean ergodic theorems for the solutions of 1 1 in hilbert space the first theorem theorem 3 1 deals with weak almost convergence and the second theorem 3 4 with strong almost convergence these results improve upon those of 1 and include the known results for nonlinear semigroups 191 it is important to establish almost convergence because it then follows that the solution is summed by every strongly regular kernel corollaries 3 3 and 3 5 a weak convergence criterion corollary 3 2 is also obtained if the banach space x is reflexive and strictly convex and 0 e r a then

a cartesian grid embedded boundary method for hyperbolic conservation laws we present a second order godunov algorithm to solve time dependent hyperbolic systems of conservation laws on irregular domains our approach is based on a formally consistent discretization of the conservation laws on a finite volume grid obtained from intersecting the domain with a cartesian grid we address the small cell stability problem associated with such methods by hybridizing our conservative discretization with a stable nonconservative discretization at irregular control volumes and redistributing the difference in the mass increments to nearby cells in a way that preserves stability and local conservation the resulting method is second order accurate in l 1 for smooth problems and is robust in the presence of large amplitude discontinuities intersecting the irregular boundary

asymptotic behavior of solutions of nonlinear volterra equations and mean points abstract in this paper we study the asymptotic behavior of solutions to a nonlinear volterra equation in banach spaces first we deal with the mean point concerning an invariant mean on 0 for the unbounded behavior of solutions in a reflexive banach space using the mean point we obtain the weak and strong convergences for the unbounded behavior of solutions in a reflexive and strictly convex banach space and in the dual space which has a frechet differentiable norm respectively

two dimensional elliptic grid solver using boundary grid control and curvature correction the thompson method of explicitly evaluating control function of the elliptic grid solver is employed to improve local grid quality around convex and concave boundaries the curvature correction is principally added to the grid lines around a boundary and is quickly attenuated as the grid points move inward the algebraic advancing front method is employed to estimate two levels of orthogonal grids for evaluating the control functions at the boundary if the grid equation based on the cauchy riemann relation with and as independent variables is employed numerical examinations show that a lengthy trial and error procedure is required to get a satisfactory grid distribution in contrast the method based on the cauchy riemann relation with x and y as independent variables which benefits from the maximum principle not only removes the undesired grid clustering and diluting easily but also effectively improves overall grid smoothness and slightly enhances boundary grid orthogonality

fourier spectral embedded boundary solution of the poisson s and laplace equations with dirichlet boundary conditions a fourier spectral embedded boundary method for solution of the poisson s equation with dirichlet boundary conditions and arbitrary forcing functions including zero forcing function is presented in this paper this iterative method begins by transformation of the dirichlet boundary conditions from the physical boundaries to some corresponding regular grid points which are called the numerical boundaries using a second order interpolation method then the transformed boundary conditions and the forcing function are extended to a square smoothly and periodically via multiplying them by some suitable error functions instead of direct solution of the resulting extended poisson s problem it is suggested to define and solve an equivalent transient diffusion problem on the regular domain until achievement of the steady solution which is considered as the solution of the original problem without need of any numerical time integration method time advancement of the solution is obtained directly from the exact solution of the transient problem in the fourier space consequently timestep sizes can be chosen without stability limitations which it means higher rates of convergence in comparison with the classical relaxation methods the method is presented in details for one and two dimensional problems and a new emerged phenomenon which is called the saturation state is illustrated both in the physical and spectral spaces the numerical experiments have been performed on the one and two dimensional irregular domains to show the accuracy of the method and its superiority from the rate of convergence viewpoint to the other classical relaxation methods capability of the method in dealing with complex geometries and in presence of discontinuity at the boundaries has been shown via some numerical experiments on a four leaf shape geometry

boundary fitted coordinate systems for numerical solution of partial differential equations a review a comprehensive review of methods of numerically generating curvilinear coordinate systems with coordinate lines coincident with all boundary segments is given some general mathematical framework and error analysis common to such coordinate systems is also included the general categories of generating systems are those based on conformal mapping orthogonal systems nearly orthogonal systems systems produced as the solution of elliptic and hyperbolic partial differential equations and systems generated algebraically by interpolation among the boundaries also covered are the control of coordinate line spacing by functions embedded in the partial differential operators of the generating system and by subsequent stretching transformation dynamically adaptive coordinate systems coupled with the physical solution and time dependent systems that follow moving boundaries are treated references reporting experience using such coordinate systems are reviewed as well as those covering the system development

structured mesh adaption space accuracy and interpolation methods abstract in this paper we review the main stages of the construction of a variational method to optimize and to adapt two and three dimensional structured grids the formalism and the notation presented enable a constructive and comprehensive description of the adaption process the major part of this paper is devoted to the study of various interpolation methods which are used for the correct space localization of the adaption for cell center cell vertex recovery and for overlapping grids interpolation in particular the behavior of the linear interpolation least square minimization and taylor series expansion methods are investigated several examples of the methods described and the combination of adaption and interpolation are presented showing their possibilities

on the asymptotic behavior of nonlinear semigroups and the range of accretive operators ii abstract it is known that certain problems in partial differential equations may be interpreted as initial value problems for ordinary differential equations in banach spaces when such an evolution equation is governed by an accretive operator then its solutions give rise to a nonlinear contraction semigroup in this paper we study certain aspects of the asymptotic behavior of nonlinear semigroups and or resolvents of accretive operators we also derive new results on their behavior at the origin it turns out that the behavior of a nonlinear semigroup resembles that of the resolvent of its generator both at infinity and at the origin author

α regularization of the pod galerkin dynamical systems of the kuramoto sivashinsky equation abstract in order to improve the dynamics and stability of the pod galerkin models of strongly stiff systems an like regularization is suggested and assessed in the present article in this method the pod eigenmodes of the non linear terms are replaced by their helmholtz filtered counterparts while the other terms are remained unchanged as an example the method is applied to the pod galerkin models of the one dimensional kuramoto sivashinsky ks equation in a full chaotic regime and the fidelity of the original and regularized models to the direct numerical simulations dns are investigated moreover the effects of regularization on the dynamics of various terms and whole of the systems are analyzed via eigenvalue analysis of each term separately and the total dynamical system as a whole the numerical experiments show definite effectiveness of the method and excellent improvements in the predicted dynamics and stability by minimum number of free parameters

high order unstructured curved mesh generation using the winslow equations we propose a method to generate high order unstructured curved meshes using the classical winslow equations we start with an initial straight sided mesh in a reference domain and fix the position of the nodes on the boundary on the true curved geometry in the interior of the domain we solve the winslow equations using a new continuous galerkin finite element discretization this formulation appears to produce high quality curved elements which are highly resistant to inversion in addition the corresponding nonlinear equations can be solved efficiently using picard iterations even for highly stretched boundary layer meshes compared to several previously proposed techniques such as optimization and approaches based on elasticity analogies this can significantly reduce the computational cost while producing curved elements of similar quality we show a number of examples in both two and three space dimensions including complex geometries and stretched boundary layers and demonstrate the high quality of the generated meshes and the performance of the nonlinear solver

a spectral embedding method applied to the advection diffusion equation in order to solve partial differential equations in complex geometries with a spectral type method one describes an embedding approach which essentially makes use of fourier expansions and boundary integral equations for the advection diffusion equation the method is based on an efficient helmholtz solver the accuracy of which is tested by considering 1d and 2d helmholtz like problems finally the capabilities of the method are pointed out by considering a 2d advection diffusion problem in a hexagonal geometry

a cartesian grid method for modeling multiple moving objects in 2d incompressible viscous flow we present an efficient method for solving 2d incompressible viscous flows around multiple moving objects our method employs an underlying regular cartesian grid to solve the system using a streamfunction vorticity formulation and with discontinuities representing the embedded objects the no penentration condition for the moving geometry is satisfied by superposing a homogenous solution to the poisson s equation for the streamfunction the no slip condition is satisfied by generating vorticity on the surfaces of the objects both the initial poisson solution and the evaluation of the homogenous solution require embedding irregular discontinuities in a fast poisson solver computation time is dictated by the time required to do a fast poisson solution plus solve an integral form of laplace s equation there is no significant increase in computational cost if the geometry of the embedded objects is variable and moving relative to the underlying grid we test the method against the canonical example of flow past a cylinder and obtained new results on the flow and forces of two cylinders moving relative to each other

a high order immersed interface method for simulating unsteady incompressible flows on irregular domains immersed boundary methods and immersed interface methods are becoming increasingly popular for the computation of unsteady flows around complex geometries using a cartesian grid while good results both qualitative and quantitative have been obtained most of the methods rely on low order corrections to account for the immersed boundary the objective of the present work is to present as an alternative a high order modified immersed interface method for the 2d unsteady incompressible navier stokes equations in stream function vorticity formulation the method employs an explicit fourth order runge kutta time integration scheme fourth order compact finite differences for computation of spatial derivatives and a nine point fourth order compact discretization of the poisson equation for computation of the stream function corrections to the finite difference schemes are used to maintain high formal accuracy at the immersed boundary as confirmed by analytical tests to validate the method in its application to incompressible flows several physically relevant test cases are computed including uniform flow past a circular cylinder and tollmien schlichting waves in a boundary layer

interactive method of variational grid generation abstract in the paper the elliptic variational grid generation technique based on methods of optimal control for distributed systems is presented the interactive nature of the method consists in adaptive changing of the golas of correction steps in the process of grid generation the corrections concern orthogonality and uniformity of the mesh

on the order of accuracy of the immersed boundary method higher order convergence rates for sufficiently smooth problems the immersed boundary method is both a mathematical formulation and a numerical scheme for problems involving the interaction of a viscous incompressible fluid and a visco elastic structure in m c lai simulations of the flow past an array of circular cylinders as a test of the immersed boundary method ph d thesis courant institute of mathematical sciences new york university 1998 m c lai c s peskin an immersed boundary method with formal second order accuracy and reduced numerical viscosity j comput phys 160 2000 705 719 lai and peskin introduced a formally second order accurate immersed boundary method but the convergence properties of their algorithm have only been examined computationally for problems with nonsmooth solutions consequently in practice only first order convergence rates have been observed in the present work we describe a new formally second order accurate immersed boundary method and demonstrate its performance for a prototypical fluid structure interaction problem involving an immersed viscoelastic shell of finite thickness studied over a broad range of reynolds numbers we consider two sets of material properties for the viscoelastic structure including a case where the material properties of the coupled system are discontinuous at the fluid structure interface for both sets of material properties the true solutions appear to possess sufficient smoothness for the method to converge at a second order rate for fully resolved computations

fourier embedded domain methods extending a function defined on an irregular region to a rectangle so that the extension is spatially periodic and c a simple way to solve a partial differential equation in a non rectangular domain w is to embed the domain in a rectangle b and solve the problem more easily in the rectangle to apply a fourier spectral method on the rectangle it is necessary to extend the inhomogeneous term in the pde f x y to b in such a way that the extended function g x y is periodic and infinitely differentiable and yet is equal to f x y everywhere in the irregular domain w if the boundary of w email protected is defined as the zero isoline of a function f x y then a suitable extension is g x y f x y h email protected x y constant where h is a smoothed approximation to the step function which is defined in the main text

on the asymptotic behavior of solutions of nonlinear volterra equations where a is an m accretive operator in x b is a given real kernel and g is a given x valued function in what follows we make the same assumptions on b and g as in 2 5 71 hl beac r r b o o b ebv r r h2 ge w r y g el r x g o ed a h3 b is completely positive on r and b m 0 we may assume without loss of generality that b 0 1 sine b t and a may be replaced by b t b o and b o a respectively note that if h 1 holds the first statement in h3 is equivalent to the fact that there exists a k e l r r nonnegative and nonincreasing satisfying b t k b t 1 for t e r moreover in this case lim o b t b cc exists and b m 0 if and only if kel r r see 2 5 71 now define g u for u e c r x or c 0 t x t 0 as follows

a cartesian grid embedded boundary method for poisson s equation on irregular domains we present a numerical method for solving poisson s equation with variable coefficients and dirichlet boundary conditions on two dimensional regions the approach uses a finite volume discretization which embeds the domain in a regular cartesian grid we treat the solution as a cell centered quantity even when those centers are outside the domain cells that contain a portion of the domain boundary use conservative differencing of second order accurate fluxes on each cell volume the calculation of the boundary flux ensures that the conditioning of the matrix is relatively unaffected by small cell volumes this allows us to use multigrid iterations with a simple point relaxation strategy we have combined this with an adaptive mesh refinement amr procedure we provide evidence that the algorithm is second order accurate on various exact solutions and compare the adaptive and nonadaptive calculations

fourier embedded domain methods periodic and c extension of a function defined on an irregular region to a rectangle via convolution with gaussian kernels abstract one possible way to solve a partial differential equation in an irregular region is the use of the so called domain embedding methods in where the domain of interest is embedded within a rectangle in order to apply a fourier spectral method on the rectangle the inhomogeneous term f x y has to be extended to a new function g x y that is periodic and infinitely differentiable and equal to f x y everywhere within some authors have given explicit methods to compute extensions with infinite order convergence for the cases in where the boundary of can be defined as the zero isoline of a function x y for the cases in where this is not possible we suggest a new method to build these extensions via convolution with gaussian kernels

solution adaptive grid generation using parabolic partial differential equations a solution adaptive parabolic grid generation scheme has been developed a new upwind finite volume formulation for space marching solution of the steady euler equations is also presented in addition a solution adaptive elliptic grid scheme developed previously and applied to unsteady flow solutions is applied in the present steady flow context solutions for hypersonic flow are computed with the present finite volume formulation coupled to both the parabolic and elliptic adaptive grid schemes the results show that the solution adaptive parabolic scheme produces grids that track the flow features of interest as well as the elliptic grid procedure this is significant because the parabolic procedure is much faster than an elliptic scheme producing a grid in an order of magnitude of less computational time

immersed boundary smooth extension the immersed boundary method is a simple efficient and robust numerical scheme for solving pde in general domains yet it only achieves first order spatial accuracy near embedded boundaries in this paper we introduce a new high order numerical method which we call the immersed boundary smooth extension ibse method the ibse method achieves high order accuracy by smoothly extending the unknown solution of the pde from a given smooth domain to a larger computational domain enabling the use of simple cartesian grid discretizations e g fourier spectral methods the method preserves much of the flexibility and robustness of the original ib method in particular it requires minimal geometric information to describe the boundary and relies only on convolution with regularized delta functions to communicate information between the computational grid and the boundary we present a fast algorithm for solving elliptic equations which forms the basis for simple high order implicit time methods for parabolic pde and implicit explicit methods for related nonlinear pde we apply the ibse method to solve the poisson heat burgers and fitzhugh nagumo equations and demonstrate fourth order pointwise convergence for dirichlet problems and third order pointwise convergence for neumann problems

immersed boundary smooth extension ibse a high order method for solving incompressible flows in arbitrary smooth domains abstract the immersed boundary method is a simple efficient and robust numerical scheme for solving pde in general domains yet for fluid problems it only achieves first order spatial accuracy near embedded boundaries for the velocity field and fails to converge pointwise for elements of the stress tensor in a previous work we introduced the immersed boundary smooth extension ibse method a variation of the ib method that achieves high order accuracy for elliptic pde by smoothly extending the unknown solution of the pde from a given smooth domain to a larger computational domain enabling the use of simple cartesian grid discretizations in this work we extend the ibse method to allow for the imposition of a divergence constraint and demonstrate high order convergence for the stokes and incompressible navier stokes equations up to third order pointwise convergence for the velocity field and second order pointwise convergence for all elements of the stress tensor the method is flexible to the underlying discretization we demonstrate solutions produced using both a fourier spectral discretization and a standard second order finite difference discretization

applications and generalizations of variational methods for generating adaptive meshes abstract generating computation meshes for irregular regions have been of interest to a lot of people in many areas of research for a long time one technique that has met with sucess over the long run has been to generate methods using an elliptic equation or a system of elliptic equations the technique in its simplest form uses a system of laplace equations which are solved by direct or iterative methods as people gained more experience with this method source terms were added to the laplace equations to gain additional control of the mesh in variable coefficients of the derivatives were added for further flexibility in this paper the authors work with a method that systematically generates a set of elliptic equations without having to explicitly perturb a set of laplace equations with source terms and variable coefficients this technique uses the variational methods often associated with elliptic equations following this introduction they briefly discuss the variational formulation in two dimensional cartesian geometry then the formulation will be generalized to three dimensions next several three dimensional test problems will be shown after displaying these three dimensional test results the author wil the exhibit an application of the mesh generation technique in two dimensions this application involves generating an adaptive mesh for a supersonic flow past a step in a wind tunnel author

on the resolution power of fourier extensions for oscillatory functions functions that are smooth but non periodic on a certain interval possess fourier series that lack uniform convergence and suffer from the gibbs phenomenon however they can be represented accurately by a fourier series that is periodic on a larger interval this is commonly called a fourier extension when constructed in a particular manner fourier extensions share many of the same features of a standard fourier series in particular one can compute fourier extensions which converge spectrally fast whenever the function is smooth and geometrically fast if the function is analytic much the same as the fourier series of a smooth analytic and periodic function with this in mind the purpose of this paper is to describe analyse and explain the observation that fourier extensions much like classical fourier series also have excellent resolution properties for representing oscillatory functions the resolution power or required number of degrees of freedom per wavelength depends on a user controlled parameter and as we show it varies between 2 and p the former value is optimal and is achieved by classical fourier series for periodic functions for example the latter value is the resolution power of algebraic polynomial approximations thus fourier extensions with an appropriate choice of parameter are eminently suitable for problems with moderate to high degrees of oscillation

elliptic grid generation various types of generating systems for boundary conforming coordinate systems based on the numerical solution of systems of elliptic partial differential equations are discussed particular emphasis is given to the determination of functions in these equations which control the distribution of the curvilinear coordinate lines in the field

spectral methods for partial differential equations in irregular domains the spectral smoothed boundary method in this paper we propose a numerical method to approximate the solution of partial differential equations in irregular domains with no flux boundary conditions the idea is to embed the domain into a box and use a smoothing term to encode the boundary conditions into a modified equation that can be approached by standard spectral methods the main features of this method are its capability to deal with domains of arbitrary shape and its easy implementation via fast fourier transform routines we discuss several examples of practical interest and test the results against standard numerical methods

the embedded finite difference method for the poisson equation in a domain with an irregular boundary and dirichlet boundary conditions the poisson equation subject to dirichlet boundary conditions on an irregular domain can be treated by embedding the region in a rectangular domain and solving using finite differences over the rectangle the crucial issue is the discretization of the boundaries of the irregular domain in the past both linear and quadratic boundary treatments have been used and error bounds have been derived in both cases showing that the linear case gives uniform second order accuracy whereas the quadratic case gives third order accuracy at the boundaries and second order accuracy internally thus it has been recommended that the linear boundary treatment be used as it is simpler gives rise to a symmetric matrix formulation and has uniform accuracy the present work shows that this argument is inadequate because the coefficients of the error terms also play an important role we demonstrate this in the 1 d case by determining explicit expressions for the error for both the linear and quadratic boundary treatments it is shown that for the linear case the coefficient of error is in general large enough to dominate the calculation and that therefore it is necessary to use a quadratic boundary treatment in order to obtain errors comparable with those obtained for a regular domain we go on to show that the 1 d expressions for error can be used to approximate the boundary error for 2 d problems and that for the linear treatment the boundary error again dominates

high order unconditionally stable fc ad solvers for general smooth domains i basic elements we introduce a new methodology for the numerical solution of partial differential equations in general spatial domains our algorithms are based on the use of the well known alternating direction implicit adi approach in conjunction with a certain fourier continuation fc method for the resolution of the gibbs phenomenon unlike previous alternating direction methods of order higher than one which can only deliver unconditional stability for rectangular domains the present high order algorithms possess the desirable property of unconditional stability for general domains the computational time required by our algorithms to advance a solution by one time step in turn grows in an essentially linear manner with the number of spatial discretization points used in this paper we demonstrate the fc ad methodology through a variety of examples concerning the heat and laplace equations in two and three dimensional domains with smooth boundaries applications of the fc ad methodology to hyperbolic pdes together with a theoretical discussion of the method will be put forth in a subsequent contribution the numerical examples presented in this text demonstrate the unconditional stability and high order convergence of the proposed algorithms as well the very significant improvements they can provide in one of our examples we demonstrate a one thousand improvement factor over the computing times required by some of the most efficient alternative general domain solvers

a priori grid quality estimation for high order finite differencing structured grids using the finite differencing method contain two sources of grid induced truncation errors the first is dependent on the solution field the second is related only to the metrics of the grid transformation the accuracy of the grid transformation metrics is affected by the inverse metrics which are spatial derivatives of the grid in the generalised coordinates the truncation errors contained in the inverse metrics are generated by the spatial schemes fourier analysis shows that the dispersion errors by spatial schemes have similarities to the transfer function of spatial filters this similarity is exploited to define a grid quality metric that can be used to identify areas in the mesh that are likely to generate significant grid induced errors an inviscid vortex convection benchmark case is used to quantify the correlation between the grid quality metric and the solution accuracy for three common geometric features found in grids abrupt changes in the grid metrics skewness and grid stretching a strong correlation is obtained provided that the grid transformation errors are the most significant sources of error

on the asymptotic behavior of solutions of evolution equations associated with nonlinear volterra equations soit x un espace de banach reel on considere le probleme aux valeurs initiales f t du t dt au t g u t r 0 u 0 u 0 ou a est un operateur m accretif dans x f l loc 1 r x u 0 d a et g une application donnee