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

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:356

Article

Neilan, Michael¹  Wu, Mohan¹ 

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

关键词: Non-divergence form;    Miranda-Talenti;    Hamilton-Jacobi-Bellman;    Finite element methods;    Convergence analysis;   

DOI  :  10.1016/j.cam.2019.01.032

来源: Elsevier

【 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.

【 授权许可】

Free