@Article{IJNAM-16-2,
author = {Xiaobing, Feng and Stefan, Schnake},
title = {A Discontinuous Ritz Method for a Class of Calculus of Variations Problems},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2019},
volume = {16},
number = {2},
pages = {340--356},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {2617-8710},
doi = {https://doi.org/2019-IJNAM-12807},
url = {https://global-sci.com/article/83068/a-discontinuous-ritz-method-for-a-class-of-calculus-of-variations-problems}
}