A Space-Time DPG Method for the Heat Equation

2020/12/24 by Diening, Lars, Storn, Johannes
#35K20 #65M12 #65M15 #65M50 #65M60 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2012.13229

Abstract

This paper introduces an ultra-weak space-time DPG method for the heat equation. We prove well-posedness of the variational formulation with broken test functions and verify quasi-optimality of a practical DPG scheme. Numerical experiments visualize beneficial properties of an adaptive and parabolically scaled mesh-refinement driven by the built-in error control of the DPG method.

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