Numerical solution of parabolic problems based on a weak space-time formulation
Journal article, 2017

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 L2 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.

Error Estimate




Finite Element




Stig Larsson

Chalmers, Mathematical Sciences, Mathematics

University of Gothenburg

Matteo Molteni

Chalmers, Mathematical Sciences, Mathematics

University of Gothenburg

Computational Methods in Applied Mathematics

1609-4840 (ISSN) 1609-9389 (eISSN)

Vol. e-pub ahead of print 1 65-84

Subject Categories

Computational Mathematics


Basic sciences



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