Piecewise solenoidal vector fields and the Stokes problem
SIAM Journal on Numerical Analysis
On a finite-element method for solving the three-dimensional Maxwell equations
Journal of Computational Physics
On a cell entropy inequality for discontinuous Galerkin methods
Mathematics of Computation
The origin of spurious solutions in computational electromagnetics
Journal of Computational Physics
A Nonconforming Finite Element Method for the Stationary Navier--Stokes Equations
SIAM Journal on Numerical Analysis
The Runge-Kutta discontinuous Galerkin method for conservation laws V multidimensional systems
Journal of Computational Physics
A negative-norm least squares method for Reissner-Mindlin plates
Mathematics of Computation
Convergence analysis of a covolume scheme for Maxwell's equations in three dimensions
Mathematics of Computation
The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
SIAM Journal on Numerical Analysis
Journal of Computational Physics
Divergence correction techniques for Maxwell solvers based on a hyperbolic model
Journal of Computational Physics
Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems
Journal of Scientific Computing
Finite Element Method for Elliptic Problems
Finite Element Method for Elliptic Problems
Nodal high-order methods on unstructured grids
Journal of Computational Physics
Enhanced accuracy by post-processing for finite element methods for hyperbolic equations
Mathematics of Computation
SIAM Journal on Scientific Computing
Journal of Computational Physics
Locally Divergence-Free Discontinuous Galerkin Methods for MHD Equations
Journal of Scientific Computing
Locally divergence-free discontinuous Galerkin methods for MHD equations
Journal of Scientific Computing
Moving Mesh Discontinuous Galerkin Method for Hyperbolic Conservation Laws
Journal of Scientific Computing
Viscous stabilization of discontinuous Galerkin solutions of hyperbolic conservation laws
Applied Numerical Mathematics - The third international conference on the numerical solutions of volterra and delay equations, May 2004, Tempe, AZ
Journal of Computational Physics
Discontinuous Galerkin method based on non-polynomial approximation spaces
Journal of Computational Physics
Interior penalty discontinuous Galerkin method for Maxwell's equations: Energy norm error estimates
Journal of Computational and Applied Mathematics
Error analysis of mixed finite element methods for wave propagation in double negative metamaterials
Journal of Computational and Applied Mathematics
Journal of Scientific Computing
Journal of Computational Physics
Superconvergence of discontinuous Galerkin methods for hyperbolic systems
Journal of Computational and Applied Mathematics
High Order Strong Stability Preserving Time Discretizations
Journal of Scientific Computing
Viscous stabilization of discontinuous Galerkin solutions of hyperbolic conservation laws
Applied Numerical Mathematics
Interior Penalty Discontinuous Galerkin Method for Maxwell's Equations in Cold Plasma
Journal of Scientific Computing
A Central Discontinuous Galerkin Method for Hamilton-Jacobi Equations
Journal of Scientific Computing
Error analysis of a discontinuous Galerkin method for Maxwell equations in dispersive media
Journal of Computational Physics
Journal of Scientific Computing
Hybridizable discontinuous Galerkin methods for the time-harmonic Maxwell's equations
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational and Applied Mathematics
Journal of Computational Physics
Well-conditioned Orthonormal Hierarchical $\mathcal{L}_{2}$ Bases on Rn Simplicial Elements
Journal of Scientific Computing
A divergence-free finite element method for a type of 3D Maxwell equations
Applied Numerical Mathematics
On the Negative-Order Norm Accuracy of a Local-Structure-Preserving LDG Method
Journal of Scientific Computing
Developing Finite Element Methods for Maxwell's Equations in a Cole-Cole Dispersive Medium
SIAM Journal on Scientific Computing
Numerical Study of the Plasma-Lorentz Model in Metamaterials
Journal of Scientific Computing
Journal of Computational Physics
Journal of Scientific Computing
Journal of Computational Physics
Numerical study of the effect of defect layer on unmagnetized plasma photonic crystals
Journal of Computational Electronics
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In this paper, we develop the locally divergence-free discontinuous Galerkin method for numerically solving the Maxwell equations. The distinctive feature of the method is the use of approximate solutions that are exactly divergence-free inside each element. As a consequence, this method has a smaller computational cost than that of the discontinuous Galerkin method with standard piecewise polynomial spaces. We show that, in spite of this fact, it produces approximations of the same accuracy. We also show that this method is more efficient than the discontinuous Galerkin method using globally divergence-free piecewise polynomial bases. Finally, a post-processing technique is used to recover (2k + 1)th order of accuracy when piecewise polynomials of degree k are used.