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

Superconvergence

Petrov–Galerkin

Quasi-Optimality

Finite Element

Space-Time

Inf-Sup

Author

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

Roots

Basic sciences

DOI

10.1515/cmam-2016-0027

More information

Latest update

3/3/2020 4