Superconvergence of Discontinuous Galerkin Methods for Elliptic Boundary Value Problems

被引：1
|
作者：
Ma, Limin [1 ]
机构：
[1] Penn State Univ, Dept Math, State Coll, PA 16802 USA
来源：
JOURNAL OF SCIENTIFIC COMPUTING | 2021年 / 88卷 / 03期
关键词：
Superconvergence; Postprocessing; Discontinuous Galerkin; Linear elasticity problem; MIXED FINITE-ELEMENTS; LINEAR ELASTICITY; HDG METHODS; RAVIART; FAMILY;
D O I：
10.1007/s10915-021-01589-7
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we present a unified analysis of the superconvergence property for a large class of mixed discontinuous Galerkin methods. This analysis applies to both the Poisson equation and linear elasticity problems with symmetric stress formulations. Based on this result, some locally postprocess schemes are employed to improve the accuracy of displacement by order min(k + 1, 2) if polynomials of degree k are employed for displacement. Some numerical experiments are carried out to validate the theoretical results.
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页数：20
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