Expanded mixed finite element methods for linear second-order elliptic problems

被引:0
作者
Chen, ZX [1 ]
机构
[1] So Methodist Univ, Dept Math, Dallas, TX 75275 USA
来源
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE | 1998年 / 32卷 / 04期
关键词
mixed method; finite element; implementation; superconvergence; error estimate; second-order elliptic problem;
D O I
暂无
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We develop a new mixed formulation for the numerical solution of second-order elliptic problems. This new formulation expands the standard mixed formulation in the sense that three variables are explicitly treated: the scalar unknown, its gradient, and its pur (the coefficient times the gradient). Based on this formulation, mixed finite element approximations of the second-order elliptic problems are considered. Optimal order error estimates in the L-P- and H- (S)-norms are obtained for the mixed approximations. Various implementation techniques for solving the systems of algebraic equations are discussed. A postprocessing method for improving the scalar variable is analyzed and superconvergent estimates in the L-P-norm are derived. The mixed formulation is suitable for the case where the coefficient of differential equations is a small tensor and does not need to be inverted. (C) Elsevier, Paris.
引用
收藏
页码:479 / 499
页数:21
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