Interior penalty method for the indefinite time-harmonic Maxwell equations
In this paper, we introduce and analyze the interior penalty discontinuous Galerkin method
for the numerical discretization of the indefinite time-harmonic Maxwell equations in the high-
frequency regime. Based on suitable duality arguments, we derive a-priori error bounds in
the energy norm and the L 2-norm. In particular, the error in the energy norm is shown to
converge with the optimal order (h min {s, ℓ}) with respect to the mesh size h, the polynomial
degree ℓ, and the regularity exponent s of the analytical solution. Under additional regularity …
for the numerical discretization of the indefinite time-harmonic Maxwell equations in the high-
frequency regime. Based on suitable duality arguments, we derive a-priori error bounds in
the energy norm and the L 2-norm. In particular, the error in the energy norm is shown to
converge with the optimal order (h min {s, ℓ}) with respect to the mesh size h, the polynomial
degree ℓ, and the regularity exponent s of the analytical solution. Under additional regularity …
Summary
In this paper, we introduce and analyze the interior penalty discontinuous Galerkin method for the numerical discretization of the indefinite time-harmonic Maxwell equations in the high-frequency regime. Based on suitable duality arguments, we derive a-priori error bounds in the energy norm and the L2-norm. In particular, the error in the energy norm is shown to converge with the optimal order (hmin{ s ,ℓ}) with respect to the mesh size h, the polynomial degree ℓ, and the regularity exponent s of the analytical solution. Under additional regularity assumptions, the L2-error is shown to converge with the optimal order (hℓ+1). The theoretical results are confirmed in a series of numerical experiments.
Springer
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