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Explicit Runge-Kutta schemes and finite elements with symmetric stabilization for first-order linear PDE systems
journal contribution
posted on 2023-06-07, 22:50 authored by Erik Burman, Alexandre Ern, Miguel A FernándezWe analyze explicit Runge-Kutta schemes in time combined with stabilized finite elements in space to approximate evolution problems with a first-order linear differential operator in space of Friedrichs-type. For the time discretization, we consider explicit second- and third-order Runge¿Kutta schemes. We identify a general set of properties on the spatial stabilization, encompassing continuous and discontinuous finite elements, under which we prove stability estimates using energy arguments. Then, we establish L^2-norm error estimates with (quasi-)optimal convergence rates for smooth solutions in space and time. These results hold under the usual CFL condition for third-order Runge¿Kutta schemes and any polynomial degree in space and for second-order Runge¿Kutta schemes and first-order polynomials in space. For second-order Runge¿Kutta schemes and higher polynomial degrees in space, a tightened 4/3-CFL condition is required. Numerical results are presented for the advection and wave equations
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Publication status
- Published
Journal
SIAM Journal on Numerical AnalysisISSN
0036-1429Publisher
Society for Industrial and Applied MathematicsExternal DOI
Issue
6Volume
48Page range
2019-2042Pages
24.0Department affiliated with
- Mathematics Publications
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- No
Peer reviewed?
- Yes
Legacy Posted Date
2012-02-06Usage metrics
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