Year: 2019
Author: Xiaobing Feng, Stefan Schnake
International Journal of Numerical Analysis and Modeling, Vol. 16 (2019), Iss. 2 : pp. 340–356
Abstract
This paper develops an analogue (or counterpart) to discontinuous Galerkin (DG) methods for approximating a general class of calculus of variations problems. The proposed method, called the discontinuous Ritz (DR) method, constructs a numerical solution by minimizing a discrete energy over DG function spaces. The discrete energy includes standard penalization terms as well as the DG finite element (DG-FE) numerical derivatives developed recently by Feng, Lewis, and Neilan in [7]. It is proved that the proposed DR method converges and that the DG-FE numerical derivatives exhibit a compactness property which is desirable and crucial for applying the proposed DR method to problems with more complex energy functionals. Numerical tests are provided on the classical $p$-Laplace problem to gauge the performance of the proposed DR method.
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2019-IJNAM-12807
International Journal of Numerical Analysis and Modeling, Vol. 16 (2019), Iss. 2 : pp. 340–356
Published online: 2019-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: Variational problems minimizers discontinuous Galerkin (DG) methods DG finite element numerical calculus compactness convergence.