A Posteriori Error Estimates for Weak Galerkin Finite Element Methods for Second Order Elliptic Problems

被引：64

作者：

Chen, Long ^{[1
]}

Wang, Junping ^{[2
]}

Ye, Xiu ^{[3
]}

机构：

[1] Univ Calif Irvine, Dept Math, Irvine, CA 92697 USA

[2] Natl Sci Fdn, Div Math Sci, Arlington, VA 22230 USA

[3] Univ Arkansas, Dept Math, Little Rock, AR 72204 USA

来源：

JOURNAL OF SCIENTIFIC COMPUTING | 2014年 / 59卷 / 02期

基金：

美国国家科学基金会;

关键词：

Weak Galerkin; Finite element methods; Discrete weak gradient; Secondorder elliptic problems; A posterior error estimate; REFINEMENT;

D O I：

10.1007/s10915-013-9771-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A residual type a posteriori error estimator is presented and analyzed for Weak Galerkin finite element methods for second order elliptic problems. The error estimator is proved to be efficient and reliable through two estimates, one from below and the other from above, in terms of an -equivalent norm for the exact error. Two numerical experiments are conducted to demonstrate the effectiveness of adaptive mesh refinement guided by this estimator.

引用

页码：496 / 511

页数：16

共 50 条

[41] Weak-Galerkin finite element methods for a second-order elliptic variational inequality
Guan, Qingguang
Gunzburger, Max
Zhao, Wenju
[J]. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2018, 337 : 677 - 688
[42] A posteriori error estimates for fourth order hyperbolic control problems by mixed finite element methods
Hou, Chunjuan
Guo, Zhanwei
Guo, Lianhong
[J]. BOUNDARY VALUE PROBLEMS, 2019, 2019 (1)
[43] A posteriori error estimates for nonconforming finite element methods for fourth-order problems on rectangles
Carstensen, Carsten
Gallistl, Dietmar
Hu, Jun
[J]. NUMERISCHE MATHEMATIK, 2013, 124 (02) : 309 - 335
[44] A posteriori error estimates for nonconforming finite element methods for fourth-order problems on rectangles
Carsten Carstensen
Dietmar Gallistl
Jun Hu
[J]. Numerische Mathematik, 2013, 124 : 309 - 335
[45] A posteriori error estimates for fourth order hyperbolic control problems by mixed finite element methods
Chunjuan Hou
Zhanwei Guo
Lianhong Guo
[J]. Boundary Value Problems, 2019
[46] Couplings of mixed finite element and weak Galerkin methods for elliptic problems
Yang M.
[J]. J. Appl. Math. Comp., 1-2 (327-343): : 327 - 343
[47] A POSTERIORI ERROR ESTIMATES FOR A LOCAL DISCONTINUOUS GALERKIN APPROXIMATION OF SEMILINEAR SECOND-ORDER ELLIPTIC PROBLEMS ON CARTESIAN GRIDS
Baccouch, Mahboub
[J]. INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING, 2023, 20 (06) : 772 - 804
[48] Localized pointwise a posteriori error estimates for gradients of piecewise linear finite element approximations to second-order quasilinear elliptic problems
Demlow, Alan
[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS, 2006, 44 (02) : 494 - 514
[49] A Posteriori Error Estimates of Edge Residual-Type of Weak Galerkin Mixed FEM Solving Second-Order Elliptic Problems on Polytopal Mesh
Wang, Huijuan
Xu, Shipeng
He, Xiaoxiao
[J]. INTERNATIONAL JOURNAL OF COMPUTATIONAL METHODS, 2022, 19 (05)
[50] Discontinuous Galerkin Finite Volume Element Methods for Second-Order Linear Elliptic Problems
Kumar, Sarvesh
Nataraj, Neela
Pani, Amiya K.
[J]. NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2009, 25 (06) : 1402 - 1424

← 1 2 3 4 5 →