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Frerichs-Mihov, Derk; John, Volker

On a technique for reducing spurious oscillations in DG solutions of convection-diffusion equations. (English) Zbl 1524.65798

Appl. Math. Lett. 129, Article ID 107969, 7 p. (2022).
Summary: This note studies a generalization of a post-processing technique and a novel method inspired by the same technique which significantly reduce spurious oscillations in discontinuous Galerkin solutions of convection-diffusion equations in the convection-dominated regime.

Cited in 2 Documents

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
76M10 Finite element methods applied to problems in fluid mechanics
35J25 Boundary value problems for second-order elliptic equations
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
76R50 Diffusion
35Q35 PDEs in connection with fluid mechanics

Keywords:

convection-diffusion equations; discontinuous Galerkin methods; spurious oscillations; post-processing techniques; slope limiter

Software:

ParMooN
Cite Review PDF
Full Text: DOI

References:

[1] Roos, Hans-Görg; Stynes, Martin; Tobiaska, Lutz, (Robust Numerical Methods For Singularly Perturbed Differential Equations: Convection-Diffusion-Reaction And Flow Problems. Robust Numerical Methods For Singularly Perturbed Differential Equations: Convection-Diffusion-Reaction And Flow Problems, Springer Series in Computational Mathematics, vol. 24 (2008), Springer Berlin Heidelberg), URL http://link.springer.com/10.1007/978-3-540-34467-4 · Zbl 1155.65087
[2] John, Volker; Knobloch, Petr, On spurious oscillations at layers diminishing (SOLD) methods for convection-diffusion equations. I. A review, Comput. Methods Appl. Mech. Engrg., 196, 17-20, 2197-2215 (2007), 2302890 (2007m:76105) · Zbl 1173.76342
[3] Jha, Abhinav; John, Volker, A study of solvers for nonlinear AFC discretizations of convection-diffusion equations, Comput. Math. Appl., 78, 9, 3117-3138 (2019), 4015770 · Zbl 1443.65343
[4] Gopalakrishnan, Jay; Kanschat, Guido, A multilevel discontinuous Galerkin method, Numer. Math., 95, 3, 527-550 (2003), 2012931 · Zbl 1044.65084
[5] Cockburn, Bernardo; Shu, Chi-Wang, The Runge-Kutta discontinuous Galerkin method for conservation laws. V. Multidimensional systems, J. Comput. Phys., 141, 2, 199-224 (1998), 1619652 · Zbl 0920.65059
[6] Dolejší, Vít; Feistauer, Miloslav; Schwab, Christoph, On discontinuous Galerkin methods for nonlinear convection-diffusion problems and compressible flow, Math. Bohem., 127, 2, 163-179 (2002) · Zbl 1074.65522
[7] Dolejší, Vít; Feistauer, Miloslav; Schwab, Christoph, On some aspects of the discontinuous Galerkin finite element method for conservation laws, Math. Comput. Simulation, 61, 3-6, 333-346 (2003), 1984135 · Zbl 1013.65108
[8] Riviére, Bèatrice, (Discontinuous Galerkin Methods For Solving Elliptic And Parabolic Equations: Theory And Implementation. Discontinuous Galerkin Methods For Solving Elliptic And Parabolic Equations: Theory And Implementation, Frontiers in Applied Mathematics, vol. 35 (2008), Society for Industrial and Applied Mathematics), URL http://epubs.siam.org/doi/book/10.1137/1.9780898717440 · Zbl 1153.65112
[9] Frerichs, Derk; John, Volker, On reducing spurious oscillations in discontinuous Galerkin (DG) methods for steady-state convection-diffusion equations, J. Comput. Appl. Math., 393, 20 (2021), Paper No. 113487. 4225710 · Zbl 1468.65188
[10] Wilbrandt, Ulrich; Bartsch, Clemens; Ahmed, Naveed; Alia, Najib; Anker, Felix; Blank, Laura; Caiazzo, Alfonso; Ganesan, Sashikumaar; Giere, Swetlana; Matthies, Gunar; Meesala, Raviteja; Shamim, Abdus; Venkatesan, Jagannath; John, Volker, Parmoon—A modernized program package based on mapped finite elements, Comput. Math. Appl., 74, 1, 74-88 (2017), 3654085 · Zbl 1375.65158
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