High-Order Numerical Methods for 2D Parabolic Problems in Single and Composite Domains
Artikel i vetenskaplig tidskrift, 2018

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.


Difference potentials

Parabolic problems

Higher order accuracy and convergence

Interface models

Spectral approach

Level set

Immersed boundary

SBP–SAT finite difference

Cut elements

Finite element method

Discontinuous solutions

Complex geometry


Gustav Ludvigsson

Uppsala universitet

Kyle R. Steffen

University of Utah

Simon Sticko

Uppsala universitet

Siyang Wang

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

Qing Xia

University of Utah

Yekaterina Epshteyn

University of Utah

Gunilla Kreiss

Uppsala universitet

Journal of Scientific Computing

0885-7474 (ISSN) 1573-7691 (eISSN)

Vol. 76 2 812-847


Teknisk mekanik


Matematisk analys



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