Space-time FEM-BEM couplings for parabolic transmission problems
Thomas F\"uhrer, Gregor Gantner, Michael Karkulik
TL;DR
This paper introduces a novel coupling of space-time FOSLS and BEM methods to efficiently solve parabolic transmission problems, with theoretical validation and numerical experiments confirming its effectiveness.
Contribution
It presents a new coupling approach combining FOSLS and BEM for parabolic problems, demonstrating coercivity and providing a validated numerical framework.
Findings
Coercivity of the coupling under specific conditions
Successful numerical validation of the theoretical approach
Effective solution of parabolic transmission problems
Abstract
We develop couplings of a recent space-time first-order system least-squares (FOSLS) method for parabolic problems and space-time boundary element methods (BEM) for the heat equation to numerically solve a parabolic transmission problem on the full space and a finite time interval. In particular, we demonstrate coercivity of the couplings under certain restrictions and validate our theoretical findings by numerical experiments.
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Taxonomy
TopicsElectromagnetic Simulation and Numerical Methods · Advanced Numerical Methods in Computational Mathematics · Numerical methods for differential equations