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A Posteriori Analysis for Space-Time, discontinuous in time Galerkin approximations for parabolic equations in a variable domain
Antonopoulou, Dimitra Plexousakis, Michael
Antonopoulou, Dimitra
Plexousakis, Michael
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2019-04-24
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Abstract
This paper presents an a posteriori error analysis for the discontinuous in time space-time scheme proposed by Jamet for the heat equation in multi-dimensional, non-cylindrical domains [25]. Using a Cl ement-type interpolant, we prove abstract a posteriori error bounds for the numerical error. Furthermore, in the case of two-dimensional spatial domains we transform the problem into an equivalent one, of parabolic type, with space-time dependent coe cients but posed on a cylindrical domain. We formulate a discontinuous in time space{time scheme and prove a posteriori error bounds of optimal order. The a priori estimates of [19] for general parabolic initial and boundary value problems are used in the derivation of the upper bound. Our lower bound coincides with that of Picasso [36], proposed for adaptive, Runge-Kutta finite element methods for linear parabolic problems. Our theoretical results are verified by numerical experiments.
Citation
Antonopoulou, D. C., & Plexousakis, M. (2019). A Posteriori Analysis for Space-Time, discontinuous in time Galerkin approximations for parabolic equations in a variable domain. ESAIM: M2AN, 53(2), 523-549.
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ECP sciences
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ESAIM: M2AN
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DOI
10.1051/m2an/2018059
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PubMed Central ID
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Article
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en
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ISSN
0764-583X
EISSN
1290-3841