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arXiv · 1603.03210

Numerical solution of parabolic problems based on a weak space-time formulation

Stig Larsson·Matteo Molteni
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Abstract

We investigate a weak space-time formulation of the heat equation and its use for the construction of a numerical scheme. The formulation is based on a known weak space-time formulation, with the difference that a pointwise component of the solution, which in other works is usually neglected, is now kept. We investigate the role of such a component by first using it to obtain a pointwise bound on the solution and then deploying it to construct a numerical scheme. The scheme obtained, besides being quasi-optimal in the $L^2$ sense, is also pointwise superconvergent in the temporal nodes. We prove a priori error estimates and we present numerical experiments to empirically support our findings.

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Stig Larsson, Matteo Molteni. 2016-03-10. Numerical solution of parabolic problems based on a weak space-time formulation. https://doi.org/10.1515/cmam-2016-0027

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