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

04/20/2020
by   Lars Diening, et al.
0

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.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 1

page 2

page 3

page 4

10/10/2019

P_1–nonconforming polyhedral finite elements in high dimensions

We consider the lowest–degree nonconforming finite element methods for t...
09/30/2019

H^1-norm error estimate for a nonstandard finite element approximation of second-order linear elliptic PDEs in non-divergence form

This paper establishes the optimal H^1-norm error estimate for a nonstan...
03/09/2021

The pointwise stabilities of piecewise linear finite element method on non-obtuse tetrahedral meshes of nonconvex polyhedra

Let Ω be a Lipschitz polyhedral (can be nonconvex) domain in ℝ^3, and V_...
10/28/2021

Adaptive finite element approximations for elliptic problems using regularized forcing data

We propose an adaptive finite element algorithm to approximate solutions...
01/08/2021

Projection in negative norms and the regularization of rough linear functionals

In order to construct regularizations of continuous linear functionals a...
02/01/2018

Slate: extending Firedrake's domain-specific abstraction to hybridized solvers for geoscience and beyond

Within the finite element community, discontinuous Galerkin (DG) and mix...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.