Work

A Priori error estimates of Runge–Kutta discontinuous Galerkin schemes to smooth solutions of fractional conservation laws

Year: 2024

Type: article

Abstract: 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.

Source: ESAIM Mathematical Modelling and Numerical Analysis

DOI: 10.1051/m2an/2024043

Authors: Fabio Leotta, Jan Giesselmann

Institution: Technische Universität Darmstadt

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid:

Funder: Deutsche Forschungsgemeinschaft