Burman, Erik;
(2023)
Some Observations on the Interaction Between Linear and Nonlinear Stabilization for Continuous Finite Element Methods Applied to Hyperbolic Conservation Laws.
SIAM Journal on Scientific Computing
, 45
(1)
A96-A122.
10.1137/21m1464154.
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Abstract
We discuss stability and accuracy of stabilized finite element methods for hyperbolic problems. In particular we focus on the interaction between linear and nonlinear stabilizations. First we show that the combination of linear and nonlinear stabilization can be designed to be invariant preserving. Then we show that such a combined method allows for the classical O(hk+12) error estimates for smooth solutions of space semidiscretized formulations of the linear transport equation. Based on these ideas we propose a Runge–Kutta finite element method for the compressible Euler equations using entropy viscosity to ensure stability at shocks and gradient jump penalty to prevent propagation of high frequency content into the smooth part of the solution. In a numerical example we show that the method predicts the shock structure accurately, without high frequency pollution of the smooth parts.
| Type: | Article |
|---|---|
| Title: | Some Observations on the Interaction Between Linear and Nonlinear Stabilization for Continuous Finite Element Methods Applied to Hyperbolic Conservation Laws |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1137/21m1464154 |
| Publisher version: | https://doi.org/10.1137/21M1464154 |
| Language: | English |
| Additional information: | This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | continuous finite elements, stability, scalar hyperbolic transport equations, compressible Euler equations, stabilized methods |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10164111 |
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