Properties of some weighted Sobolev spaces and application to spectral approximations
SIAM Journal on Numerical Analysis
The Fourier-Finite-Element Method for Poisson's Equation in Axisymmetric Domains with Edges
SIAM Journal on Numerical Analysis
Finite Element Method for Elliptic Problems
Finite Element Method for Elliptic Problems
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Axisymmetric Stokes equations in polygonal domains: Regularity and finite element approximations
Computers & Mathematics with Applications
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This paper analyzes the effects of conical points on the rotation axis of axisymmetric domains Ω ⊂ R3 on the regularity of the Fourier coefficients un (n ∈ Z) of the solution u of the Dirichlet problem for the Poisson equation -Δu = f in Ω. The asymptotic behavior of the coefficients un, near the conical points is carefully described and for f ∈ L2(Ω), it is proved that if the interior opening angle θc at the conical point is greater than a certain critical angle θ*, then the regularity of the coefficient u0 will be lower than expected. Moreover, it is shown that conical points on the rotation axis of the axisymmetric domain do not affect the regularity of the coefficients un, n ≠ 0. An approximation of the critical angle θ* is established numerically and a priori error estimate for the Fourier-finite-element solutions in the norm of W21 (Ω) is given.