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Inf-Sup Stable Space-Time Methods for Time-Dependent Partial Differential Equations

Produktform: Buch

For the discretisation of time-dependent partial differential equations, the classical approaches are time stepping schemes together with finite element methods in space. An alternative is to discretise the time-dependent problem without separating the temporal and spatial variables. However, space-time approximation methods depend strongly on the space-time variational formulations on the continuous level. The focus of this work is on space-time variational formulations for the heat and wave equation, which result not only in inf-sup stable formulations but fit also very well to conforming space-time discretisations.The first part investigates the heat equation in anisotropic Sobolev spaces, where a type of Hilbert transform is introduced such that ansatz and test spaces are equal. Unconditional stability is proven for any conforming discretisation of this space-time variational formulation.The second part considers space-time variational formulations for the wave equation. New existence and uniqueness results for the wave equation in a weak and in a strong sense are proven, including isomorphic solution operators and corresponding inf-sup conditions. In addition, an unconditionally stable space-time finite element method with piecewise linear, continuous functions is derived.weiterlesen

Dieser Artikel gehört zu den folgenden Serien

Sprache(n): Englisch

ISBN: 978-3-85125-721-2 / 978-3851257212 / 9783851257212

Verlag: Verlag d. Technischen Universität Graz

Erscheinungsdatum: 27.02.2020

Seiten: 210

Autor(en): Marco Zank

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