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

共 36 条

[1]

Ambrosio L., 2000, OXFORD MATH MONOGRAP

[2]

[Anonymous], 2015, SPRINGER SERIES COMP

[3]

[Anonymous], 1970, CONVEX ANAL

[4]

[Anonymous], 1978, FINITE ELEMENT METHO

[5] Unified analysis of discontinuous Galerkin methods for elliptic problems [J].

Arnold, DN ;

Brezzi, F ;

Cockburn, B ;

Marini, LD .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2002, 39 (05) :1749-1779

[6] AN INTERIOR PENALTY FINITE-ELEMENT METHOD WITH DISCONTINUOUS ELEMENTS [J].

ARNOLD, DN .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1982, 19 (04) :742-760

[7]

Attouch A, 2005, MOS-SIAM SER OPTIMIZ, V6, P1

[8]

Bartels S, 2016, TEXTS APPL MATH, V64, P1, DOI 10.1007/978-3-319-32354-1

[9] A TOTAL VARIATION DIMINISHING INTERPOLATION OPERATOR AND APPLICATIONS [J].

Bartels, Soeren ;

Nochetto, Ricardo H. ;

Salgado, Abner J. .

MATHEMATICS OF COMPUTATION, 2015, 84 (296) :2569-2587

[10] DISCRETE TOTAL VARIATION FLOWS WITHOUT REGULARIZATION [J].

Bartels, Soeren ;

Nochetto, Ricardo H. ;

Salgado, Abner J. .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2014, 52 (01) :363-385

← 1 2 3 4 →