High-Order Numerical Methods for 2D Parabolic Problems in Single and Composite Domains

In this work, we discuss and compare three methods for the numerical approximation of constant- and variable-coefficient diffusion equations in both single and composite domains with possible discontinuity in the solution/flux at interfaces, considering (i) the Cut Finite Element Method; (ii) the Di...

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Vydané v:	Journal of scientific computing Ročník 76; číslo 2; s. 812 - 847
Hlavní autori:	Ludvigsson, Gustav, Steffen, Kyle R., Sticko, Simon, Wang, Siyang, Xia, Qing, Epshteyn, Yekaterina, Kreiss, Gunilla
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	New York Springer US 01.08.2018 Springer Nature B.V
Predmet:	1994 Algorithms Approximation Boundary conditions by-parts operators Complex geometry Composite materials Computational Mathematics and Numerical Analysis Cut elements Difference potentials discontinuous coefficients Discontinuous solutions elastic-wave elliptic interface problems embedded boundary method equation Finite difference method Finite element analysis Finite element method Finite volume method finite-difference methods ghost fluid method Higher order accuracy Higher order accuracy and convergence Immersed boundary interface Interface models Interfaces international journal for numerical methods in engineering irregular domains journal of computational physics Level set matched Matematik Materials science Mathematical analysis Mathematical and Computational Engineering Mathematical and Computational Physics Mathematical sciences Mathematics Mathematics and Statistics mirdzic i Numerical analysis Numerical methods p3751 p47 Parabolic problems Partial differential equations potentials method rand b SBP-SAT finite difference Spectral approach Stabilization Theoretical v110 v37 35K20 Complex geometry Level set Stabilization 65M06 Cut elements Immersed boundary Discontinuous solutions Spectral approach Difference potentials Finite element method Interface models 65M70 SBP–SAT finite difference Higher order accuracy and convergence Parabolic problems 65M60 65M22 65M55 65M12
ISSN:	0885-7474, 1573-7691, 1573-7691
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Popis
Shrnutí:	In this work, we discuss and compare three methods for the numerical approximation of constant- and variable-coefficient diffusion equations in both single and composite domains with possible discontinuity in the solution/flux at interfaces, considering (i) the Cut Finite Element Method; (ii) the Difference Potentials Method; and (iii) the summation-by-parts Finite Difference Method. First we give a brief introduction for each of the three methods. Next, we propose benchmark problems, and consider numerical tests—with respect to accuracy and convergence—for linear parabolic problems on a single domain, and continue with similar tests for linear parabolic problems on a composite domain (with the interface defined either explicitly or implicitly). Lastly, a comparative discussion of the methods and numerical results will be given.
Bibliografia:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ISSN:	0885-7474 1573-7691 1573-7691
DOI:	10.1007/s10915-017-0637-y