SUPERCONVERGENCE BY M-DECOMPOSITIONS. PART I: GENERAL THEORY FOR HDG METHODS FOR DIFFUSION

被引：39

作者：

Cockburn, Bernardo ^{[1
]}

Fu, Guosheng ^{[1
,2
]}

Sayas, Francisco Javier ^{[3
]}

机构：

[1] Univ Minnesota, Sch Math, Minneapolis, MN 55455 USA

[2] Brown Univ, Div Appl Math, Providence, RI 02912 USA

[3] Univ Delaware, Dept Math Sci, Newark, DE 19716 USA

来源：

MATHEMATICS OF COMPUTATION | 2017年 / 86卷 / 306期

基金：

美国国家科学基金会;

关键词：

2ND-ORDER ELLIPTIC PROBLEMS; MIXED FINITE-ELEMENTS; DISCONTINUOUS GALERKIN METHODS; ACOUSTIC-WAVE EQUATION; TIME SUPERCONVERGENCE; ERROR ANALYSIS; HYBRIDIZATION; ELASTICITY; ORDER;

D O I：

10.1090/mcom/3140

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We introduce the concept of an M-decomposition and show how to use it to systematically construct hybridizable discontinuous Galerkin and mixed methods for steady-state diffusion methods with superconvergence properties on unstructured meshes.

引用

页码：1609 / 1641

页数：33

共 29 条

[1] MIXED AND NONCONFORMING FINITE-ELEMENT METHODS - IMPLEMENTATION, POSTPROCESSING AND ERROR-ESTIMATES [J].

ARNOLD, DN ;

BREZZI, F .

ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 1985, 19 (01) :7-32

[2] 2 FAMILIES OF MIXED FINITE-ELEMENTS FOR 2ND ORDER ELLIPTIC PROBLEMS [J].

BREZZI, F ;

DOUGLAS, J ;

MARINI, LD .

NUMERISCHE MATHEMATIK, 1985, 47 (02) :217-235

[3]

BREZZI F, 1987, RAIRO-MATH MODEL NUM, V21, P581

[4] An a priori error analysis of the local discontinuous Galerkin method for elliptic problems [J].

Castillo, P ;

Cockburn, B ;

Perugia, I ;

Shötzau, D .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2000, 38 (05) :1676-1706

[5] UNIFORM-IN-TIME SUPERCONVERGENCE OF HDG METHODS FOR THE HEAT EQUATION [J].

Chabaud, Brandon ;

Cockburn, Bernardo .

MATHEMATICS OF COMPUTATION, 2012, 81 (277) :107-129

[6]

Chen Z., 1989, Calcolo, V26, P135, DOI 10.1007/BF02575725

[7] OPTIMAL DISCONTINUOUS GALERKIN METHODS FOR THE ACOUSTIC WAVE EQUATION IN HIGHER DIMENSIONS [J].

Chung, Eric T. ;

Engquist, Bjoern .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2009, 47 (05) :3820-3848

[8]

Cockburn B, 2009, MATH COMPUT, V78, P1

[9] A superconvergent LDG-hybridizable Galerkin method for second-order elliptic problems [J].

Cockburn, Bernardo ;

Dong, Bo ;

Guzman, Johnny .

MATHEMATICS OF COMPUTATION, 2008, 77 (264) :1887-1916

[10] Static Condensation, Hybridization, and the Devising of the HDG Methods [J].

Cockburn, Bernardo .

BUILDING BRIDGES: CONNECTIONS AND CHALLENGES IN MODERN APPROACHES TO NUMERICAL PARTIAL DIFFERENTIAL EQUATIONS, 2016, 114 :129-177

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