三角/四面体双调和方程的c0 -符合DG有限元法

IF 3.8 2区数学 Q1 MATHEMATICS

Journal of Numerical Mathematics Pub Date : 2021-12-30 DOI:10.1515/jnma-2021-0012

X. Ye, Shangyou Zhang

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引用次数: 6

摘要

摘要介绍了一种求解双调和方程的c0 -适不连续Galerkin (CDG)有限元方法。C0有限元函数的第一个强梯度是一个不连续的分段多项式向量。第二类梯度是不连续分段多项式的弱梯度。该方法顾名思义，采用非一致性(非C1)近似，保持一致性有限元方法的简单公式，不使用任何稳定器。对相应的有限元解分别建立了离散h2 -范数和l2 -范数下的最优阶误差估计。数值结果证实了收敛理论。

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A C0-conforming DG finite element method for biharmonic equations on triangle/tetrahedron

Abstract A C0-conforming discontinuous Galerkin (CDG) finite element method is introduced for solving the biharmonic equation. The first strong gradient of C0 finite element functions is a vector of discontinuous piecewise polynomials. The second gradient is the weak gradient of discontinuous piecewise polynomials. This method, by its name, uses nonconforming (non C1) approximations and keeps simple formulation of conforming finite element methods without any stabilizers. Optimal order error estimates in both a discrete H2-norm and the L2-norm are established for the corresponding finite element solutions. Numerical results are presented to confirm the theory of convergence.

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来源期刊

Journal of Numerical Mathematics 数学-数学

CiteScore

5.90

自引率

3.30%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Numerical Mathematics (formerly East-West Journal of Numerical Mathematics) contains high-quality papers featuring contemporary research in all areas of Numerical Mathematics. This includes the development, analysis, and implementation of new and innovative methods in Numerical Linear Algebra, Numerical Analysis, Optimal Control/Optimization, and Scientific Computing. The journal will also publish applications-oriented papers with significant mathematical content in computational fluid dynamics and other areas of computational engineering, finance, and life sciences.