The Fourier-Finite-Element Method for Poisson's Equation in Axisymmetric Domains with Edges
SIAM Journal on Numerical Analysis
A singular field method for the solution of Maxwell's equations in polyhedral domains
SIAM Journal on Applied Mathematics
Journal of Computational Physics
Finite Element Method for Elliptic Problems
Finite Element Method for Elliptic Problems
A Singular Field Method for Maxwell's Equations: Numerical Aspects for 2D Magnetostatics
SIAM Journal on Numerical Analysis
Journal of Computational Physics
The Fourier-finite element method for the Poisson problem on a non-convex polyhedral cylinder
Journal of Computational and Applied Mathematics
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Three-dimensional time-harmonic Maxwell's problems in axisymmetric domains @W@? with edges and conical points on the boundary are treated by means of the Fourier-finite-element method. The Fourier-fem combines the approximating Fourier series expansion of the solution with respect to the rotational angle using trigonometric polynomials of degree N(N-~), with the finite element approximation of the Fourier coefficients on the plane meridian domain @W"a@?R"+^2 of @W@? with mesh size h(h-0). The singular behaviors of the Fourier coefficients near angular points of the domain @W"a are fully described by suitable singular functions and treated numerically by means of the singular function method with the finite element method on graded meshes. It is proved that the rate of convergence of the mixed approximations in H^1(@W@?)^3 is of the order O(h+N^-^1) as known for the classical Fourier-finite-element approximation of problems with regular solutions.