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Optimal L2-Norm Error Estimates for Steady and Unsteady Maxwell Equations Using Skeletal Discontinuous Galerkin Methods
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DOI：10.1002/num.70077.png)
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Abstract
En 中文
This article proposes an optimal convergence analysis of two model problems: the stationary Maxwell equations, which represent the H(curl)-elliptic problem, and the time-dependent Maxwell equations in cold plasma. We employ skeletal discontinuous Galerkin (DG) methods for spatial discretization. First, we introduce a skeletal DG method for the H(curl)-elliptic problem with variable coefficients and discuss the optimal convergence analysis in the energy and L-2 norms. Next, we propose a continuous in time skeletal DG method for the Maxwell problem in cold plasma. The proof of error converging at an optimal rate for the cold plasma equations in L-2 and discrete energy norms hinges on a suitably defined Ritz projection derived from the previously discussed stationary Maxwell problem. We also present numerical computations in two and three dimensions for the stationary and time-dependent Maxwell equations, including implicit and explicit time integration techniques for the time-dependent case. These computations verify the theoretical rates we have presented
Keywords:
cold plasma
Maxwell equations
optimal error estimates
skeletal DG methods
Journal
N
IF:
1.7
Papers:
46
Citations:
3.9K