A space–time Trefftz discontinuous Galerkin method for the acoustic wave equation in first-order formulation

被引：0
作者：
Andrea Moiola
Ilaria Perugia
机构：
[1] University of Reading,Department of Mathematics and Statistics
[2] University of Pavia,Department of Mathematics
[3] University of Vienna,Faculty of Mathematics
来源：
Numerische Mathematik | 2018年 / 138卷
关键词：
65M60; 65M15; 41A10; 41A25; 35L05;
D O I：
暂无
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学科分类号：
摘要：
We introduce a space–time Trefftz discontinuous Galerkin method for the first-order transient acoustic wave equations in arbitrary space dimensions, extending the one-dimensional scheme of Kretzschmar et al. (IMA J Numer Anal 36:1599–1635, 2016). Test and trial discrete functions are space–time piecewise polynomial solutions of the wave equations. We prove well-posedness and a priori error bounds in both skeleton-based and mesh-independent norms. The space–time formulation corresponds to an implicit time-stepping scheme, if posed on meshes partitioned in time slabs, or to an explicit scheme, if posed on “tent-pitched” meshes. We describe two Trefftz polynomial discrete spaces, introduce bases for them and prove optimal, high-order h-convergence bounds.
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页码：389 / 435
页数：46
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