Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6928560 | Journal of Computational Physics | 2018 | 14 Pages |
Abstract
This paper studies finite element discretizations for three types of time-dependent PDEs, namely heat equation, scalar conservation law and wave equation, which we reformulate as first order systems in a least-squares setting, subject to a space-time conservation constraint (coming from the original PDE). Available piecewise polynomial finite element spaces in (n+1)-dimensions for functional spaces from the (n+1)-dimensional de Rham sequence for n=2,3 are used for the implementation of the method. Computational results illustrating the error behavior, iteration counts and performance of block-diagonal and monolithic geometric multigrid preconditioners are presented for the discrete CFOSLS system. The results are obtained from a parallel implementation of the methods for which we report reasonable scalability.
Related Topics
Physical Sciences and Engineering
Computer Science
Computer Science Applications
Authors
Kirill Voronin, Chak Shing Lee, Martin Neumüller, Paulina Sepulveda, Panayot S. Vassilevski,