Numerical solution of parabolic problems based on a weak space-time formulation
Preprint, 2016

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.

space-time

inf-sup

superconvergence

quasi-optimality

finite ele- ment

Petrov–Galerkin.

error estimate

Author

Stig Larsson

Chalmers, Mathematical Sciences, Mathematics

University of Gothenburg

Matteo Molteni

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematics

Subject Categories

Mathematics

Computational Mathematics

Roots

Basic sciences

More information

Created

10/8/2017