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A Space-Time DPG Method for the Heat Equation

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arxiv 2012.13229 v2 pith:UKI6KZWT submitted 2020-12-24 math.NA cs.NA

Lars Diening , Johannes Storn This is my paper · ORCID
classification math.NAcs.NA
keywords methodequationheatspace-timeadaptivebeneficialbrokenbuilt-in
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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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