DeepAI AI Chat
Log In Sign Up

Uniform Hölder-norm bounds for finite element approximations of second-order elliptic equations

by   Lars Diening, et al.

We develop a discrete counterpart of the De Giorgi-Nash-Moser theory, which provides uniform Hölder-norm bounds on continuous piecewise affine finite element approximations of second-order linear elliptic problems of the form -∇·(A∇ u)=f-∇· F with A∈ L^∞(Ω;R^n× n) a uniformly elliptic matrix-valued function, f∈ L^q(Ω), F∈ L^p(Ω;R^n), with p > n and q > n/2, on A-nonobtuse shape-regular triangulations, which are not required to be quasi-uniform, of a bounded polyhedral Lipschitz domain Ω⊂R^n.


page 1

page 2

page 3

page 4


Stability of mixed FEMs for non-selfadjoint indefinite second-order linear elliptic PDEs

For a well-posed non-selfadjoint indefinite second-order linear elliptic...

Finite element approximation for uniformly elliptic linear PDE of second order in nondivergence form

This paper proposes a novel technique for the approximation of strong so...

Stability and guaranteed error control of approximations to the Monge–Ampère equation

This paper analyzes a regularization scheme of the Monge–Ampère equation...

Least-Squares Methods with Nonconforming Finite Elements for General Second-Order Elliptic Equations

In this paper, we study least-squares finite element methods (LSFEM) for...

Uniform estimations for conforming Galerkin method for anisotropic singularly perturbed elliptic problems

In this article, we study some anisotropic singular perturbations for a ...

Adaptive finite element approximations for elliptic problems using regularized forcing data

We propose an adaptive finite element algorithm to approximate solutions...

Projection in negative norms and the regularization of rough linear functionals

In order to construct regularizations of continuous linear functionals a...