scholarly journals A Symplectic Discontinuous Galerkin Full Discretization for Stochastic Maxwell Equations

2021 ◽  
Vol 59 (4) ◽  
pp. 2197-2217
Author(s):  
Chuchu Chen
Keyword(s):  
Discontinuous Galerkin ◽  
Maxwell Equations ◽  
Full Discretization ◽  
Stochastic Maxwell Equations

scholarly journals The multi-dimensional Hermite-discontinuous Galerkin method for the Vlasov–Maxwell equations

2021 ◽  
Vol 264 ◽  
pp. 107866
Author(s):  
O. Koshkarov ◽  
G. Manzini ◽  
G.L. Delzanno ◽  
C. Pagliantini ◽  
V. Roytershteyn
Keyword(s):  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Maxwell Equations

scholarly journals Analysis of a hybridizable discontinuous Galerkin method for the Maxwell operator

2019 ◽  
Vol 53 (1) ◽  
pp. 301-324 ◽  
Author(s):  
Gang Chen ◽  
Jintao Cui ◽  
Liwei Xu
Keyword(s):  
Discontinuous Galerkin ◽  
Maxwell Equations ◽  
Numerical Solutions ◽  
Special Treatment ◽  
Optimal Order ◽  
General Regularity ◽  
Maxwell Operator ◽  
Low Regularity ◽  
Hybridizable Discontinuous Galerkin ◽  
Theoretical Results

In this paper, we study a hybridizable discontinuous Galerkin (HDG) method for the Maxwell operator. The only global unknowns are defined on the inter-element boundaries, and the numerical solutions are obtained by using discontinuous polynomial approximations. The error analysis is based on a mixed curl-curl formulation for the Maxwell equations. Theoretical results are obtained under a more general regularity requirement. In particular for the low regularity case, special treatment is applied to approximate data on the boundary. The HDG method is shown to be stable and convergence in an optimal order for both high and low regularity cases. Numerical experiments with both smooth and singular analytical solutions are performed to verify the theoretical results.

Sign in / Sign up

Export Citation Format

Share Document