一维不连续有限元的超收敛:弱伽辽金法

IF 1.2 4区数学 Q2 MATHEMATICS, APPLIED

East Asian Journal on Applied Mathematics Pub Date : 2022-06-01 DOI:10.4208/eajam.030921.141121

X. Ye, Shangyou Zhang

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引用次数: 4

摘要

.介绍了一种求解一维二阶椭圆问题的简单无稳定器弱Galerkin（SFWG）有限元方法。在这种方法中，弱函数由一个不连续的k阶多项式形成，该多项式在顶点上定义了额外的未知数，而其弱导数由k+1次多项式近似。建立了SFWG有限元解的二阶超收敛性。结果表明，Pk-SFWG方程的单元提升Pk+2解收敛于最优阶。数值结果证实了这一理论。

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Achieving Superconvergence by One-Dimensional Discontinuous Finite Elements: Weak Galerkin Method

. A simple stabilizer free weak Galerkin (SFWG) ﬁnite element method for a one-dimensional second order elliptic problem is introduced. In this method, the weak function is formed by a discontinuous k -th order polynomial with additional unknowns deﬁned on vertex points, whereas its weak derivative is approximated by a polynomial of degree k + 1. The superconvergence of order two for the SFWG ﬁnite element solution is established. It is shown that the elementwise lifted P k + 2 solution of the P k SFWG one converges at the optimal order. Numerical results conﬁrm the theory.

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来源期刊

East Asian Journal on Applied Mathematics MATHEMATICS, APPLIED-

CiteScore

2.60

自引率

8.30%

发文量

期刊介绍： The East Asian Journal on Applied Mathematics (EAJAM) aims at promoting study and research in Applied Mathematics in East Asia. It is the editorial policy of EAJAM to accept refereed papers in all active areas of Applied Mathematics and related Mathematical Sciences. Novel applications of Mathematics in real situations are especially welcome. Substantial survey papers on topics of exceptional interest will also be published occasionally.