The Poisson equation in axisymmetric domains with conical points
Journal of Computational and Applied Mathematics
The Fourier-finite element method for the Poisson problem on a non-convex polyhedral cylinder
Journal of Computational and Applied Mathematics
Axisymmetric Stokes equations in polygonal domains: Regularity and finite element approximations
Computers & Mathematics with Applications
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The Fourier-finite-element method, which combines the approximating Fourier and finite-element method, is applied to the Dirichlet problem of the Poisson equation $-\Delta_3 \hat u = \hat f$ in axisymmetric domains $\hat \Omega \subset R^3$ with reentrant edges. The edge singularity function is given by a suitable nontensor product representation and treated numerically by mesh grading in the two-dimensional meridian of $\hat \Omega$, with linear finite elements. For $\hat f \in L_2 (\hat \Omega)$, the rate of convergence of the combined approximation in the Sobolev spaces $H^l(\hat \Omega)\,(l=0,1)$ is proved to be of the order $O(N^{-(2-l)}+h^{2-l})$. Owing to some mixed projection and estimation techniques, the degree $N$ of trigonometric polynomials and the mesh size $h$ of the triangular mesh occurring in the error estimates are not coupled and are of the same order as is known for regular solutions $\hat u\in H^2(\hat \Omega)$. The results are illustrated by numerical experiments.