The Fourier Singular Complement Method for the Poisson Problem. Part III: Implementation Issues
This paper is the last part of a three-fold article aimed at some efficient numerical methods for solving the Poisson problem in three-dimensional prismatic and axisymmetric domains. In the first and second parts, the Fourier singular complement method (FSCM) was introduced and analysed for pr...
| Summary: | This paper is the last part of a three-fold article
aimed at some efficient numerical methods for
solving the Poisson problem in three-dimensional
prismatic and axisymmetric domains. In the first
and second parts, the Fourier singular complement
method (FSCM) was introduced and analysed for
prismatic and axisymmetric domains with reentrant
edges, as well as for the axisymmetric domains
with sharp conical vertices. In this paper we
shall mainly conduct numerical experiments to check
and compare the accuracies and efficiencies
of FSCM and some other related numerical methods
for solving the Poisson problem in the
aforementioned domains. In the case of prismatic
domains with a reentrant edge, we shall compare
the convergence rates of three numerical methods:
3D finite element method using prismatic elements,
FSCM, and the 3D finite element method combined
with the FSCM. For axisymmetric domains with a
non-convex edge or a sharp conical vertex we
investigate the convergence rates of the
Fourier finite element method (FFEM) and the
FSCM, where the FFEM will be implemented on both
quasi-uniform meshes and locally graded meshes.
The complexities of the considered algorithms
are also analysed. |
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