2021
DOI: 10.1137/20m1349060
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High Order Cut Discontinuous Galerkin Methods for Hyperbolic Conservation Laws in One Space Dimension

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Cited by 14 publications
(12 citation statements)
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“…Examining (12), we observe that for α ≥ ν there holds η k1 = 0 and therefore the stabilization J h vanishes. This is intended as in this case the standard CFL condition on cell I k1 is satisfied and we do not have a small cell problem.…”
Section: Choice Of η K1mentioning
confidence: 91%
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“…Examining (12), we observe that for α ≥ ν there holds η k1 = 0 and therefore the stabilization J h vanishes. This is intended as in this case the standard CFL condition on cell I k1 is satisfied and we do not have a small cell problem.…”
Section: Choice Of η K1mentioning
confidence: 91%
“…While there are many different approaches for stabilizing discretizations for elliptic and parabolic problems on cut cell meshes (for an overview see, e.g., [5]) the research for hyperbolic problems is still at the beginning but with a lot of current activity. Some very recent work [12,16,32] is based on applying the ghost penalty stabilization [6], which is a well-known approach for elliptic equations, to hyperbolic problems. Out of these contributions, only Fu and Kreiss [12] address the small cell problem for first-order hyperbolic problems by developing a stabilization for the solution of scalar conservation laws in one dimension.…”
Section: Introductionmentioning
confidence: 99%
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“…For hyperbolic problems, CutFEM based on discontinuous piecewise polynomial spaces and ghost penalty stabilization has been developed, e.g. see [12] where a time independent linear advection-reaction problem is considered and see [10] for time dependent nonlinear conservation laws. We also refer to the recent work [8] where a DG method for time dependent linear advection problems is developed with a stabilization of small elements that is designed to restore proper domains of dependence.…”
Section: Introductionmentioning
confidence: 99%
“…The first main result is an extension of the family of high order CutFEM with ghost penalty stabilization in [10] to problems with stationary interfaces. In the new method the solution is built from separate solutions on the two sides of the interface, and coupled through the interface condition, which is imposed weakly through penalties in the weak form.…”
Section: Introductionmentioning
confidence: 99%