ERROR ESTIMATES FOR A CLASS OF DISCONTINUOUS GALERKIN METHODS FOR NONSMOOTH PROBLEMS VIA CONVEX DUALITY RELATIONS

被引：4

作者：

Bartels, Soren ^{[1
]}

机构：

[1] Albert Ludwigs Univ Freiburg, Abt Angew Math, Hermann Herder Str 10, D-79104 Freiburg, Germany

来源：

MATHEMATICS OF COMPUTATION | 2021年 / 90卷 / 332期

关键词：

Nonsmooth problems; discontinuous Galerkin method; error estimates; total variation; variational inequalities; DISCRETE TOTAL VARIATION; FINITE-ELEMENT METHODS; REGULARITY; CALCULUS; SOBOLEV;

D O I：

10.1090/mcom/3656

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We devise and analyze a class of interior penalty discontinuous Galerkin methods for nonlinear and nonsmooth variational problems. Discrete duality relations are derived that lead to optimal error estimates in the case of total-variation regularized minimization or obstacle problems. The analysis provides explicit estimates that precisely determine the role of stabilization parameters. Numerical experiments confirm the optimality of the estimates.

引用

页码：2579 / 2602

页数：24

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