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

被引：2

作者：

Diening, Lars ^{[1
]}

Scharle, Toni ^{[2
]}

Suli, Endre ^{[2
]}

机构：

[1] Univ Bielefeld, Fac Math, Univ Str 25, D-33615 Bielefeld, Germany

[2] Univ Oxford, Math Inst, Woodstock Rd, Oxford OX2 6GG, England

来源：

IMA JOURNAL OF NUMERICAL ANALYSIS | 2021年 / 41卷 / 03期

基金：

英国工程与自然科学研究理事会;

关键词：

elliptic differential equations; finite element methods; discrete C-alpha regularity; CONVERGENCE; REGULARITY;

D O I：

10.1093/imanum/drab029

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We develop a discrete counterpart of the De Giorgi-Nash-Moser theory, which provides uniform Holder-norm bounds on continuous piecewise affine finite element approximations of second-order linear elliptic problems of the form -del center dot (A del u) = f - del center dot F with A epsilon L-infinity (Omega; R-nxn) a uniformly elliptic matrix-valued function, f epsilon L-q(Omega), F epsilon L-p(Omega; 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 Omega subset of R-n.

引用

页码：1846 / 1898

页数：53

共 31 条

[1]

Aguilera N. E., 1986, Calcolo, V23, P327, DOI 10.1007/BF02576116

[2]

[Anonymous], 1976, Numerical Solution of Partial Differential Equations-III

[3] FINITE-ELEMENT ERROR ANALYSIS OF A QUASI-NEWTONIAN FLOW OBEYING THE CARREAU OR POWER-LAW [J].