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Journal of Scientific Computing

Erschienen in:

21.08.2017

Space-Time Adaptive Methods for the Mixed Formulation of a Linear Parabolic Problem

verfasst von: Dongho Kim, Eun-Jae Park, Boyoon Seo

Erschienen in: Journal of Scientific Computing | Ausgabe 3/2018

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Abstract

In this paper, we are concerned with space-time a posteriori error estimators for fully discrete solutions of linear parabolic problems. The mixed formulation with Raviart–Thomas finite element spaces is considered. A new second-order method in time is proposed so that mixed finite element spaces are permitted to change at different time levels. The new method can be viewed as a variant Crank–Nicolson (CN) scheme. Introducing a CN reconstruction appropriate for the mixed setting, we construct an a posteriori error estimator of second order in time for the variant CN mixed scheme. Various numerical examples are given to test our space-time adaptive algorithm and validate the theory proved in the paper. In addition, numerical results for backward Euler and CN schemes are presented to compare their performance in the time adaptivity setting over uniform/adaptive spatial meshes.

Vorheriger Artikel Approximations on SO(3) by Wigner D-matrix and Applications

Nächster Artikel An Analysis of Stability of the Flux Reconstruction Formulation on Quadrilateral Elements for the Linear Advection–Diffusion Equation

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Titel: Space-Time Adaptive Methods for the Mixed Formulation of a Linear Parabolic Problem
verfasst von: Dongho Kim
Eun-Jae Park
Boyoon Seo
Publikationsdatum: 21.08.2017
Verlag: Springer US
Erschienen in: Journal of Scientific Computing / Ausgabe 3/2018
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-017-0514-8

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