On the convergence of the regularized entropy-based moment method for kinetic equations

Abstract

The entropy-based moment method is a well-known discretization for the velocity variable in kinetic equations which has many desirable theoretical properties but is difficult to implement with high-order numerical methods. The regularized entropy-based moment method was recently introduced to remove one of the main challenges in the implementation of the entropy-based moment method, namely the requirement of the realizability of the numerical solution. In this work we use the method of relative entropy to prove the convergence of the regularized method to the original method as the regularization parameter goes to zero and give convergence rates. Our main assumptions are the boundedness of the velocity domain and that the original moment solution is Lipschitz continuous in space and bounded away from the boundary of realizability. We provide results from numerical simulations showing that the convergence rates we prove are optimal.

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• Relative energy for the Korteweg theory and related Hamiltonian flows in gas dynamics
• A realizability-preserving discontinuous Galerkin scheme for entropy-based moment closures for linear kinetic equations in one space dimension
• Stability properties of the Euler-Korteweg system with nonmonotone pressures
• Criteria for the a-contraction and stability for the piecewise-smooth solutions to hyperbolic balance laws

Cited by in corpus (1)

• Convergence of hyperbolic approximations to higher-order PDEs for smooth solutions