A new family of mixed finite elements in IR3
Numerische Mathematik
Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
SIAM Journal on Numerical Analysis
Nodal high-order methods on unstructured grids
Journal of Computational Physics
Thehp-local discontinuous Galerkin method for low-frequency time-harmonic Maxwell equations
Mathematics of Computation
Locally divergence-free discontinuous Galerkin methods for the Maxwell equations
Journal of Computational Physics
Interior penalty method for the indefinite time-harmonic Maxwell equations
Numerische Mathematik
Incompressible Finite Elements via Hybridization. Part I: The Stokes System in Two Space Dimensions
SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
Journal of Scientific Computing
The Compact Discontinuous Galerkin (CDG) Method for Elliptic Problems
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Journal of Computational Physics
Computing with Hp-Adaptive Finite Elements, Vol. 2: Frontiers Three Dimensional Elliptic and Maxwell Problems with Applications
Journal of Computational Physics
The Derivation of Hybridizable Discontinuous Galerkin Methods for Stokes Flow
SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
A Hybridizable Discontinuous Galerkin Method for Steady-State Convection-Diffusion-Reaction Problems
SIAM Journal on Scientific Computing
A Comparison of HDG Methods for Stokes Flow
Journal of Scientific Computing
Journal of Computational Physics
High-order implicit hybridizable discontinuous Galerkin methods for acoustics and elastodynamics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
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We present two hybridizable discontinuous Galerkin (HDG) methods for the numerical solution of the time-harmonic Maxwell's equations. The first HDG method explicitly enforces the divergence-free condition and thus necessitates the introduction of a Lagrange multiplier. It produces a linear system for the degrees of freedom of the approximate traces of both the tangential component of the vector field and the Lagrange multiplier. The second HDG method does not explicitly enforce the divergence-free condition and thus results in a linear system for the degrees of freedom of the approximate trace of the tangential component of the vector field only. For both HDG methods, the approximate vector field converges with the optimal order of k+1 in the L^2-norm, when polynomials of degree k are used to represent all the approximate variables. We propose elementwise postprocessing to obtain a new H^c^u^r^l-conforming approximate vector field which converges with order k+1 in the H^c^u^r^l-norm. We present extensive numerical examples to demonstrate and compare the performance of the HDG methods.