Discrete Miranda-Talenti estimates and applications to linear and nonlinear PDEs

被引：20

作者：

Neilan, Michael ^{[1
]}

Wu, Mohan ^{[1
]}

机构：

[1] Univ Pittsburgh, Dept Math, Pittsburgh, PA 15260 USA

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2019年 / 356卷

基金：

美国国家科学基金会;

关键词：

Non-divergence form; Miranda-Talenti; Hamilton-Jacobi-Bellman; Finite element methods; Convergence analysis; ELLIPTIC-EQUATIONS; NUMERICAL-ANALYSIS; GALERKIN METHODS; FORM;

D O I：

10.1016/j.cam.2019.01.032

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, we construct simple and convergent finite element methods for linear and nonlinear elliptic differential equations in non-divergence form with discontinuous coefficients. The methods are motivated by discrete Miranda-Talenti estimates, which relate the H-2 semi-norm of piecewise polynomials with the L-2 norm of its Laplacian on convex domains. We develop a stability and convergence theory of the proposed methods, and back up the theory with numerical experiments. (C) 2019 Elsevier B.V. All rights reserved.

引用

页码：358 / 376

页数：19

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