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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.


This document is the unedited author's version of a submitted work that was subsequently accepted for publication in the Journal of Computational Physics. The final edited and published version of the work is available at: Journal of Computational Physics, Volume 373, 15 November 2018, Pages 863-876,



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