Stable least-squares space-time boundary element methods for the wave equation

Document detail

ID

oai:arXiv.org:2312.12547

Topic

Mathematics - Numerical Analysis

Author

Hoonhout, Daniel Löscher, Richard Steinbach, Olaf Urzúa-Torres, Carolina

Year

2023

listing date

12/27/2023

Keywords

mixed $ boundary

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Abstract

In this paper, we recast the variational formulation corresponding to the single layer boundary integral operator $\operatorname{V}$ for the wave equation as a minimization problem in $L^2(\Sigma)$, where $\Sigma := \partial \Omega \times (0,T)$ is the lateral boundary of the space-time domain $Q := \Omega \times (0,T)$.

For discretization, the minimization problem is restated as a mixed saddle point formulation.

Unique solvability is established by combining conforming nested boundary element spaces for the mixed formulation such that the related bilinear form is discrete inf-sup stable.

We analyze under which conditions the discrete inf-sup stability is satisfied, and, moreover, we show that the mixed formulation provides a simple error indicator, which can be used for adaptivity.

We present several numerical experiments showing the applicability of the method to different time-domain boundary integral formulations used in the literature.

Hoonhout, Daniel,Löscher, Richard,Steinbach, Olaf,Urzúa-Torres, Carolina, 2023, Stable least-squares space-time boundary element methods for the wave equation

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