On a finite-element method for solving the three-dimensional Maxwell equations
Journal of Computational Physics
On some techniques for approximating boundary conditions in the finite element method
Modelling 94 Proceedings of the 1994 international symposium on Mathematical modelling and computational methods
Journal of Computational Physics
A Singular Field Method for Maxwell's Equations: Numerical Aspects for 2D Magnetostatics
SIAM Journal on Numerical Analysis
Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
SIAM Journal on Numerical Analysis
Nitsche type method for approximating boundary conditions in the static Maxwell equations
MIC '07 Proceedings of the 26th IASTED International Conference on Modelling, Identification, and Control
Solving Maxwell's equations in singular domains with a Nitsche type method
Journal of Computational Physics
A Nitsche type method for stress fields calculation in dissimilar material with interface crack
Applied Numerical Mathematics
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We are concerned with the singular solution of the static Maxwell equation in a non-convex polygon. Thanks to a Hodge decomposition of the solution on a solenoidal and irrotational parts, one obtains an equivalent formulation to the static problem by solving two Laplace equations. Then a finite element formulation is derived, based on a Nitsche type method. This allows us to solve numerically the static Maxwell equation in domains with reentrant corners, where the solution can be singular. We formulate the method and report some numerical experiments. As a by product, this approach proves its ability to compute the dual singular functions of the Laplacian (see definition below).