ADAPTIVE VERTEX-CENTERED FINITE VOLUME METHODS WITH CONVERGENCE RATES

被引：13

作者：

Erath, Christoph ^{[1
]}

Praetorius, Dirk ^{[2
]}

机构：

[1] Tech Univ Darmstadt, Dept Math, D-64293 Darmstadt, Germany

[2] Vienna Univ Technol, Inst Anal & Sci Comp, Wiedner Hauptstr 8-10, A-1040 Vienna, Austria

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 2016年 / 54卷 / 04期

基金：

奥地利科学基金会;

关键词：

finite volume method; a posteriori error estimators; adaptive algorithm; local mesh-refinement; convergence; optimality; optimal convergence rates; BOUNDARY-ELEMENT METHODS; MESH REFINEMENT; APPROXIMATION;

D O I：

10.1137/15M1036701

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the vertex-centered finite volume method with first-order conforming ansatz functions. The adaptive mesh-refinement is driven by the local contributions of the weighted residual error estimator. We prove that the adaptive algorithm leads to linear convergence with generically optimal algebraic rates for the error estimator and the sum of energy error plus data oscillations. While similar results have been derived for finite element methods and boundary element methods, the present work appears to be the first for adaptive finite volume methods, where the lack of the classical Galerkin orthogonality leads to new challenges.

引用

页码：2228 / 2255

页数：28

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