Coercive space-time finite element methods for initial boundary value problems. ETNA - Electronic Transactions on Numerical Analysis
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30 mars 2020
- handle: 10670/1.1klu93
- issn: 1068-9613
- doi: 10.1553/etna_vol52s154
info:eu-repo/semantics/openAccess
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Spacetime Space-times Space of more than three dimensions Time and space Space-time Space-time continuumCiter ce document
Marco Zank et al., « Coercive space-time finite element methods for initial boundary value problems. ETNA - Electronic Transactions on Numerical Analysis », Elektronisches Publikationsportal der Österreichischen Akademie der Wissenschafte, ID : 10.1553/etna_vol52s154
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Résumé
We propose and analyse new space-time Galerkin-Bubnov-type finite element formulations of parabolic and hyperbolic second-order partial differential equations in finite time intervals. Using Hilbert-type transformations, this approach is based on elliptic reformulations of first- and second-order time derivatives, for which the Galerkin finite element discretisation results in positive definite and symmetric matrices. For the variational formulation of the heat and wave equations, we prove related stability conditions in appropriate norms, and we discuss the stability of related finite element discretisations. Numerical results are given which confirm the theoretical results.