Optimal Maximum Norm Estimates for Virtual Element Methods

Interior Maximum-norm Estimates for Finite Element Methods, Part Ii

We consider bilinear forms A(-, •) connected with second-order elliptic problems and assume that for uh in a finite element space S¡,, we have A(u U),, x) = F(x) for x m Sh with local compact support. We give local estimates for u Uf, in L^ and W^ of the type "local best approximation plus weak outside influences plus the local size of F ".

Maximum-norm estimates for resolvents of elliptic finite element operators

Let Ω be a convex domain with smooth boundary in Rd. It has been shown recently that the semigroup generated by the discrete Laplacian for quasi-uniform families of piecewise linear finite element spaces on Ω is analytic with respect to the maximum-norm, uniformly in the mesh-width. This implies a resolvent estimate of standard form in the maximum-norm outside some sector in the right halfplane...

Maximum - Norm Interior Estimates for Ritz - Galerkin Methods

In this paper we obtain, by simple means, interior maximum-norm estimates for a class of Ritz-Galerkin methods used for approximating solutions of second order elliptic boundary value problems in R . The estimates are proved when the approximating subspaces are any of a large class of piecewise polynomial subspaces which we assume here to be defined on a uniform mesh on the interior domain. Opt...

Maximum Norm Estimates in the Finite Element Method

The finite element method is considered when applied to a model Dirichlet problem on a plane polygonal domain. Rate of convergence estimates in the maximum norm, up to the boundary, are given locally. The rate of convergence may vary from point to point and is shown to depend on the local smoothness of the solution and on a possible pollution effect. In one of the applications given, a method i...

L1-error Estimates and Superconvergence in Maximum Norm of Mixed Finite Element Methods for Nonfickian Flows in Porous Media