Optimal convergence recovery for the Fourier-finite-element approximation of Maxwell's equations in nonsmooth axisymmetric domains
The paper is concerned with the numerical approximation of the time harmonic Maxwell's equations in the case of an axisymmetric domain with edges and conical points on the boundary. The method used is the Fourier-finite-element method: the solution is expanded as a Fourier series with respect to the rotational angle using trigonometric polynomials and then the Fourier coefficients on the plain meridian domain are approximated by means of the finite element method. Error estimates in the \(H^1\)-norm are given when using piecewise linear polynomial shape functions. For domains with reentrant edges and conical points, it is shown that a combination of the singular function method with the finite element method on locally graded meshes for the approximation of the two-dimensional solutions would yield an optimal convergence rate.
scientific article; zbMATH DE number 5173636
scientific article