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dc.contributor.author
Bansal, Pratyuksh
dc.contributor.author
Moiola, Andrea
dc.contributor.author
Perugia, Ilaria
dc.contributor.author
Schwab, Christoph
dc.date.accessioned
2020-08-07T11:16:28Z
dc.date.available
2020-08-04T10:25:11Z
dc.date.available
2020-08-07T11:16:28Z
dc.date.issued
2020-02
dc.identifier.uri
http://hdl.handle.net/20.500.11850/429925
dc.description.abstract
We develop a convergence theory of space--time discretizations for the linear, 2nd-order wave equation in polygonal domains Ω⊂ℝ2, possibly occupied by piecewise homogeneous media with different propagation speeds. Building on an unconditionally stable space--time DG formulation developed in~\cite{MoPe18}, we (a) prove optimal convergence rates for the space--time scheme with local isotropic corner mesh refinement on the spatial domain, and (b) demonstrate numerically optimal convergence rates of a suitable \emph{sparse} space--time version of the DG scheme. The latter scheme is based on the so-called \emph{combination formula}, in conjunction with a family of anisotropic space--time DG-discretizations. It results in optimal-order convergent schemes, also in domains with corners, with a number of degrees of freedom that scales essentially like the DG solution of one stationary elliptic problem in Ω on the finest spatial grid. Numerical experiments for both smooth and singular solutions support convergence rate optimality on spatially refined meshes of the full and sparse space--time DG schemes.
en_US
dc.language.iso
en
en_US
dc.publisher
Seminar for Applied Mathematics, ETH Zurich
en_US
dc.subject
Acoustic wave
en_US
dc.subject
Point singularities
en_US
dc.subject
Space-time DG
en_US
dc.subject
Local isotropic mesh refinement
en_US
dc.subject
Combination formula
en_US
dc.title
Space–time discontinuous Galerkin approximation of acoustic waves with point singularities
en_US
dc.type
Report
ethz.journal.title
SAM Research Report
ethz.journal.volume
2020-10
en_US
ethz.size
43 p.
en_US
ethz.grant
Computational modeling of shocks and interfaces
en_US
ethz.publication.place
Zurich
en_US
ethz.publication.status
published
en_US
ethz.leitzahl
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02000 - Dep. Mathematik / Dep. of Mathematics::02501 - Seminar für Angewandte Mathematik / Seminar for Applied Mathematics::03435 - Schwab, Christoph / Schwab, Christoph
en_US
ethz.leitzahl.certified
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02000 - Dep. Mathematik / Dep. of Mathematics::02501 - Seminar für Angewandte Mathematik / Seminar for Applied Mathematics::03435 - Schwab, Christoph / Schwab, Christoph
en_US
ethz.identifier.url
https://math.ethz.ch/sam/research/reports.html?id=883
ethz.grant.agreementno
642768
ethz.grant.fundername
SBFI
ethz.grant.funderDoi
10.13039/501100007352
ethz.grant.program
H2020
ethz.date.deposited
2020-08-04T10:25:33Z
ethz.source
FORM
ethz.eth
yes
en_US
ethz.identifier.internal
https://math.ethz.ch/sam/research/reports.html?id=883
en_US
ethz.availability
Metadata only
en_US
ethz.rosetta.installDate
2020-08-07T11:16:45Z
ethz.rosetta.lastUpdated
2020-08-07T11:16:45Z
ethz.rosetta.versionExported
true
ethz.COinS
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