Discontinuous Galerkin methods for magnetic advection-diffusion problems

@article{Wang2022DiscontinuousGM,
  title={Discontinuous Galerkin methods for magnetic advection-diffusion problems},
  author={Jin-Der Wang and Shuonan Wu},
  journal={ArXiv},
  year={2022},
  volume={abs/2208.01267}
}
. We devise and analyze a class of the primal discontinuous Galerkin methods for the magnetic advection-diffusion problems based on the weighted-residual approach. In addition to the upwind stabilization, we find a new mechanism under the vector case that provides more flexibility in constructing the schemes. For the more general Friedrichs system, we show the stability and optimal error estimate, which boil down to two core ingredients – the weight function and the special projection – that… 

Figures from this paper

References

SHOWING 1-10 OF 49 REFERENCES

Discontinuous Galerkin Methods for Advection-Diffusion-Reaction Problems

The weighted-residual approach recently introduced in Brezzi et al. is applied to derive discontinuous Galerkin formulations for advection-diffusion-reaction problems, and two new methods are proposed.

Stabilized Galerkin methods for magnetic advection

This work provides rigorous a priori error estimates for both fully discontinuous piecewise polynomial trial functions and H (curl, Ω)-conforming finite elements in boundary value problems modeling the advection of magnetic fields.

Discontinuous Galerkin Methods for Friedrichs' Systems. I. General theory

A general discontinuous Galerkin method that weakly enforces boundary conditions and mildly penalizes interface jumps is proposed, and an abstract error analysis in the spirit of Strang's Second Lemma is presented.

Stabilized Galerkin for transient advection of differential forms

A rigorous a priori convergence theory is established for Lipschitz continuous velocities, conforming meshes and standard finite element spaces of discrete differential forms for generalized transient advection problems for differential forms on bounded spatial domains.

Optimal a priori error estimates for the hp-version of the local discontinuous Galerkin method for convection-diffusion problems

Theoretical results are confirmed in a series of numerical examples and upper bounds for the energy norm of the error which are explicit in the mesh-width h, in the polynomial degree p, and in the regularity of the exact solution are obtained.

Edge stabilization for Galerkin approximations of convection?diffusion?reaction problems

Continuous interior penalty hp-finite element methods for advection and advection-diffusion equations

A continuous interior penalty hp-finite element method that penalizes the jump of the discrete solution across mesh interfaces is introduced. Error estimates are obtained for first-order and