Data di Pubblicazione:
2016
Citazione:
The L2-projection and quasi-optimality of Galerkin methods for parabolic equations / F. Tantardini, A. Veeser. - In: SIAM JOURNAL ON NUMERICAL ANALYSIS. - ISSN 0036-1429. - 54:1(2016), pp. 317-340.
Abstract:
We consider linear parabolic initial-boundary value problems and analyze Galerkin approximation in space. With the help of the inf-sup theory, we derive quasi-optimality results with respect to norms that arise from the standard weak formulation and from a formulation requiring only integrability in time. Moreover, we reveal that the H1-stability of the L2-projection is not only sufficient but also necessary for these results. As application, we consider conforming finite element approximation in space and derive a priori error bounds in terms of the local meshsize and piecewise regularity. The regularity is the minimal one indicated by approximation theory and matches regularity results for linear parabolic problems.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
finite element methods; Galerkin approximations; L2-projection; parabolic initial-boundary value problems; quasi-optimality; numerical analysis
Elenco autori:
F. Tantardini, A. Veeser
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