This work was supported by the ARO under US Army Federal Grant # W911NF-15-1-0590 and # W911NF-16-1-0307. Numerical studies were partially facilitated by equipment acquired under NSFs Major Research Instrumentation grant DMS-1624776. Part of this work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.
Finite element method, Inequalities (Mathematics)
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 piece- wise polynomial finite element spaces in (n + 1)-dimensions for functional spaces from the (n + 1)-dimensional de Rham sequence for n = 3, 4 are used for the implementation of the method. Computational results illustrating the error behavior, iteration counts and performance of block-diagonal and monolithic geometric multi- grid 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.
Voronin, Kirill; Lee, Chak Shing; Neumüller, Martin; Sepulveda, Paulina; and Vassilevski, Panayot S., "Space-Time Discretizations Using Constrained First-Order System Least Squares (CFOSLS)" (2018). Portland Institute for Computational Science Publications. 4.