ADAPTIVE FEM WITH OPTIMAL CONVERGENCE RATES FOR A CERTAIN CLASS OF NONSYMMETRIC AND POSSIBLY NONLINEAR PROBLEMS

被引：57

作者：

Feischl, M. ^{[1
]}

Fuehrer, T. ^{[1
]}

Praetorius, D. ^{[1
]}

机构：

[1] Vienna Univ Technol, Inst Anal & Sci Comp, A-1040 Vienna, Austria

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 2014年 / 52卷 / 02期

基金：

奥地利科学基金会;

关键词：

adaptive algorithm; convergence; optimal cardinality; nonlinear; nonsymmetric; FINITE-ELEMENT-METHOD; INHOMOGENEOUS DIRICHLET DATA; EQUATION;

D O I：

10.1137/120897225

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We analyze adaptive mesh-refining algorithms for conforming finite element discretizations of certain nonlinear second-order partial differential equations. We allow continuous polynomials of arbitrary but fixed polynomial order. The adaptivity is driven by the residual error estimator. We prove convergence even with optimal algebraic convergence rates. In particular, our analysis covers general linear second-order elliptic operators. Unlike prior works for linear nonsymmetric operators, our analysis avoids the interior node property for the refinement, and the differential operator has to satisfy a Garding inequality only. If the differential operator is uniformly elliptic, no additional assumption on the initial mesh is posed.

引用

页码：601 / 625

页数：25