| Issue |
ESAIM: M2AN
Volume 58, Number 4, July-August 2024
|
|
|---|---|---|
| Page(s) | 1301 - 1315 | |
| DOI | https://doi.org/10.1051/m2an/2024043 | |
| Published online | 30 July 2024 | |
A Priori error estimates of Runge–Kutta discontinuous Galerkin schemes to smooth solutions of fractional conservation laws
Department of Mathematics, Technical University Darmstadt, Darmstadt, Germany
* Corresponding author: leotta@mathematik.tu-darmstadt.de
Received:
23
February
2024
Accepted:
25
May
2024
We give a priori error estimates of second order in time fully explicit Runge–Kutta discontinuous Galerkin schemes using upwind fluxes to smooth solutions of scalar fractional conservation laws in one space dimension. Under the time step restrictions τ ≤ ch for piecewise linear and τ ≲ h4/3 for higher order finite elements, we prove a convergence rate for the energy norm ‖⋅‖Lt∞Lx2+|⋅|Lx2Hxλ/2 that is optimal for solutions and flux functions that are smooth enough. Our proof relies on a novel upwind projection of the exact solution.
Mathematics Subject Classification: 35 / 65 / 65N12 / 65N15
Key words: A priori error estimation / fractional convection-diffusion / fractional conservation laws / hyperbolic conservation laws / discontinuous Galerkin method
© The authors. Published by EDP Sciences, SMAI 2024
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