AN A POSTERIORI ERROR ANALYSIS OF MIXED FINITE ELEMENT GALERKIN APPROXIMATIONS TO SECOND ORDER LINEAR PARABOLIC PROBLEMS

被引：12

作者：

Memon, Sajid ^{[1
]}

Nataraj, Neela ^{[1
]}

Pani, Amiya Kumar ^{[1
]}

机构：

[1] Indian Inst Technol, Dept Math, Bombay 400076, Maharashtra, India

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 2012年 / 50卷 / 03期

关键词：

a posteriori error estimates; mixed finite element method; linear parabolic equation; mixed elliptic reconstructions; backward Euler; adaptive algorithms; ELLIPTIC RECONSTRUCTION; DIFFERENTIAL-EQUATIONS; NONLINEAR PROBLEMS; DISCRETIZATIONS; MODEL;

D O I：

10.1137/100782760

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, a posteriori error estimates are derived for mixed finite element Galerkin approximations to second order linear parabolic initial and boundary value problems. Using mixed elliptic reconstructions, a posteriori error estimates in L infinity(L-2)- and L-2(L-2)-norms for the solution as well as its flux are proved for the semidiscrete scheme. Finally, based on a backward Euler method, a completely discrete scheme is analyzed and a posteriori error bounds are derived, which improves upon earlier results on a posteriori estimates of mixed finite element approximations to parabolic problems. Results of numerical experiments verifying the efficiency of the estimators have also been provided.

引用

页码：1367 / 1393

页数：27

共 50 条

[1] A POSTERIORI ERROR ESTIMATES FOR MIXED FINITE ELEMENT GALERKIN APPROXIMATIONS TO SECOND ORDER LINEAR HYPERBOLIC EQUATIONS
Karaa, Samir
Pani, Amiya K.
[J]. INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING, 2017, 14 (4-5) : 571 - 590
[2] A posteriori error estimates for mixed finite element approximations of parabolic problems
Larson, Mats G.
Malqvist, Axel
[J]. NUMERISCHE MATHEMATIK, 2011, 118 (01) : 33 - 48
[3] A posteriori error estimates for mixed finite element approximations of parabolic problems
Mats G. Larson
Axel Målqvist
[J]. Numerische Mathematik, 2011, 118 : 33 - 48
[4] A priori and a posteriori error analysis for the mixed discontinuous Galerkin finite element approximations of the biharmonic problems
Xiong, Chunguang
Becker, Roland
Luo, Fusheng
Ma, Xiuling
[J]. NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2017, 33 (01) : 318 - 353
[5] A Posteriori Error Estimates for Weak Galerkin Finite Element Methods for Second Order Elliptic Problems
Chen, Long
Wang, Junping
Ye, Xiu
[J]. JOURNAL OF SCIENTIFIC COMPUTING, 2014, 59 (02) : 496 - 511
[6] A Posteriori Error Estimates for Weak Galerkin Finite Element Methods for Second Order Elliptic Problems
Long Chen
Junping Wang
Xiu Ye
[J]. Journal of Scientific Computing, 2014, 59 : 496 - 511
[7] A priori and a posteriori error analysis for discontinuous Galerkin finite element approximations of biharmonic eigenvalue problems
Wang, Liang
Xiong, Chunguang
Wu, Huibin
Luo, Fusheng
[J]. ADVANCES IN COMPUTATIONAL MATHEMATICS, 2019, 45 (5-6) : 2623 - 2646
[8] A priori and a posteriori error analysis for discontinuous Galerkin finite element approximations of biharmonic eigenvalue problems
Liang Wang
Chunguang Xiong
Huibin Wu
Fusheng Luo
[J]. Advances in Computational Mathematics, 2019, 45 : 2623 - 2646
[9] A posteriori error estimates of the weak Galerkin finite element methods for parabolic problems
Dai, Jiajia
Chen, Luoping
Yang, Miao
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2024, 445
[10] A posteriori error estimates for mixed finite element approximations of elliptic problems
Mats G. Larson
Axel Målqvist
[J]. Numerische Mathematik, 2008, 108 : 487 - 500

← 1 2 3 4 5 →