High-Order Numerical Methods for 2D Parabolic Problems in Single and Composite Domains
Journal article, 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.
Stabilization
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
Author
Gustav Ludvigsson
Uppsala University
Kyle R. Steffen
University of Utah
Simon Sticko
Uppsala University
Siyang Wang
Chalmers, Mathematical Sciences, Applied Mathematics and Statistics
Qing Xia
University of Utah
Yekaterina Epshteyn
University of Utah
Gunilla Kreiss
Uppsala University
Journal of Scientific Computing
0885-7474 (ISSN) 1573-7691 (eISSN)
Vol. 76 2 812-847Subject Categories
Applied Mechanics
Computational Mathematics
Mathematical Analysis
DOI
10.1007/s10915-017-0637-y