Pointwise error estimates and asymptotic error expansion inequalities for the finite element method on irregular grids: Part I. Global estimates

Pointwise error estimates and asymptotic error expansion inequalities for the finite element method on irregular grids: Part I. Global estimates

This part contains new pointwise error estimates for the finite element method for second order elliptic boundary value problems on smooth bounded domains in RN . In a sense to be discussed below these sharpen known quasi–optimal L∞ and W 1 ∞ estimates for the error on irregular quasi–uniform meshes in that they indicate a more local dependence of the error at a point on the derivatives of the ...

Pointwise localized error estimates for parabolic finite element equations

Localized pointwise error estimates for mixed finite element methods

In this paper we give weighted, or localized, pointwise error estimates which are valid for two different mixed finite element methods for a general second-order linear elliptic problem and for general choices of mixed elements for simplicial meshes. These estimates, similar in spirit to those recently proved by Schatz for the basic Galerkin finite element method for elliptic problems, show tha...

Error Estimates for the Finite Element Solutions of Variational Inequalities

For plecewise linear approximation of variational inequalities associated with the mildly nonlinear elliptic boundary value problems having auxiliary constraint conditions, we prove that the error estimate for u-uh in the W 1’2norm is of order h. KEV WORDS AND PHRASES. Fine Element, V)nal Inequalities, Approximation, Mdly nonlinear. 1980 THEMATICS SUBJECT CLASSIFICATION CODES. Primary 5J20, 65N...

A note on entropy inequalities and error estimates for higher-order accurate finite volume schemes on irregular families of grids

Recently, Cockburn, Coquel and LeFloch proved convergence and error estimates for higher-order finite volume schemes. Their result is based on entropy inequalities which are derived under restrictive assumptions on either the flux function or the numerical fluxes. Moreover, they assume that the spatial grid satisfies a standard regularity assumption. Using instead entropy inequalities derived i...