We present a second order time-stepping scheme for parabolic problems on moving domains and interfaces. The diffusion coefficient is discontinuous and jumps across an interior interface. This causes the solution to have discontinuous derivatives in space and time. Without special treatment of the interface, both spatial and temporal discretization will be sub-optimal. For such problems, we develop a time-stepping method, based on a cG(1) Eulerian space-time Galerkin approach. We show −both analytically and numerically− second order convergence in time. Key to gaining the optimal order of convergence is the use of space-time test- and trial-functions, that are aligned with the moving interface. Possible applications are multiphase flow or fluid-structure interaction problems.
Accepté le :
DOI : 10.1051/m2an/2016072
Keywords: Space-time finite elements, time stepping, moving interfaces, a priori error analysis
Frei, Stefan 1 ; Richter, Thomas 2
@article{M2AN_2017__51_4_1539_0,
author = {Frei, Stefan and Richter, Thomas},
title = {A second order time-stepping scheme for parabolic interface problems with moving interfaces},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {1539--1560},
year = {2017},
publisher = {EDP Sciences},
volume = {51},
number = {4},
doi = {10.1051/m2an/2016072},
mrnumber = {3702424},
zbl = {1379.65076},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an/2016072/}
}
TY - JOUR AU - Frei, Stefan AU - Richter, Thomas TI - A second order time-stepping scheme for parabolic interface problems with moving interfaces JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2017 SP - 1539 EP - 1560 VL - 51 IS - 4 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/m2an/2016072/ DO - 10.1051/m2an/2016072 LA - en ID - M2AN_2017__51_4_1539_0 ER -
%0 Journal Article %A Frei, Stefan %A Richter, Thomas %T A second order time-stepping scheme for parabolic interface problems with moving interfaces %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2017 %P 1539-1560 %V 51 %N 4 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/m2an/2016072/ %R 10.1051/m2an/2016072 %G en %F M2AN_2017__51_4_1539_0
Frei, Stefan; Richter, Thomas. A second order time-stepping scheme for parabolic interface problems with moving interfaces. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 51 (2017) no. 4, pp. 1539-1560. doi: 10.1051/m2an/2016072
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