Superconvergence and accuracy enhancement of discontinuous Galerkin solutions for VlasovMaxwell equations
Abstract
This paper considers the discontinuous Galerkin (DG) methods for solving the VlasovMaxwell (VM) system, a fundamental model for collisionless magnetized plasma. The DG methods provide accurate numerical description with conservation and stability properties. However, to resolve the high dimensional probability distribution function, the computational cost is the main bottleneck even for modernday supercomputers. This work studies the applicability of a postprocessing technique to the DG solution to enhance its accuracy and resolution for the VM system. In particular, we prove the superconvergence of order $(2k+\frac{1}{2})$ in the negative order norm for the probability distribution function and the electromagnetic fields when piecewise polynomial degree $k$ is used. Numerical tests including Landau damping, twostream instability and streaming Weibel instabilities are considered showing the performance of the postprocessor.
 Publication:

arXiv eprints
 Pub Date:
 October 2022
 DOI:
 10.48550/arXiv.2210.07908
 arXiv:
 arXiv:2210.07908
 Bibcode:
 2022arXiv221007908G
 Keywords:

 Mathematics  Numerical Analysis