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

Stig Larsson (Institutionen för matematiska vetenskaper, matematik) ; Matteo Molteni (Institutionen för matematiska vetenskaper, matematik)
Computational Methods in Applied Mathematics (1609-4840). Vol. e-pub ahead of print (2016),
[Artikel, refereegranskad vetenskaplig]

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.

Nyckelord: Inf-Sup, Space-Time, Superconvergence, Quasi-Optimality, Finite Element, Error Estimate, Petrov–Galerkin



Denna post skapades 2016-10-16. Senast ändrad 2016-10-19.
CPL Pubid: 243465

 

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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematik (2005-2016)

Ämnesområden

Numerisk analys

Chalmers infrastruktur