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

Författare

Stig Larsson

Chalmers, Matematiska vetenskaper, Matematik

Göteborgs universitet

Matteo Molteni

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Matematik

Ämneskategorier

Matematik

Beräkningsmatematik

Fundament

Grundläggande vetenskaper

Mer information

Skapat

2017-10-08