Spectral collocation on triangular elements

DOI10.1006/jcph.1998.6052zbMath0909.65089OpenAlexW1998935636MaRDI QIDQ1268371

Wilhelm Heinrichs

Publication date: 22 March 1999

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jcph.1998.6052

zbMATH Keywords

domain decompositionpreconditioningfinite differencesingular solutionsiterative solverspectral collocation methodChebyshev collocation methodtriangular elementauxiliary mapping

Mathematics Subject Classification ID

Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Iterative numerical methods for linear systems (65F10) Numerical computation of matrix norms, conditioning, scaling (65F35) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

Related Items (13)

Spectral collocation schemes on the unit disc ⋮ Assessment of finite and spectral element shape functions for efficient iterative simulations of interior acoustics ⋮ An adaptive least-squares spectral collocation method with triangular elements for the incompressible Navier-Stokes equations ⋮ Error analysis of spectral method on a triangle ⋮ A triangular spectral element method for elliptic and Stokes problems ⋮ A spectral-element method for particulate Stokes flow ⋮ Overlapping Schwarz methods for unstructured spectral elements ⋮ Spectral Schemes on Triangular Elements ⋮ Optimal error estimates in Jacobi-weighted Sobolev spaces for polynomial approximations on the triangle ⋮ Interfacial dynamics for Stokes flow. ⋮ Improved Lebesgue constants on the triangle ⋮ Spectral schemes on triangular elements ⋮ A pseudo-spectral scheme for the incompressible Navier-Stokes equations using unstructured nodal elements

Cites Work

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• Spectral methods on triangles and other domains
• Stable spectral methods for conservation laws on triangles with unstructured grids
• The optimal symmetrical points for polynomial interpolation of real functions in the tetrahedron
• Spectral element methods for elliptic problems in nonsmooth domains
• Tetrahedral \(hp\) finite elements: Algorithms and flow simulations
• Approximate optimal points for polynomial interpolation of real functions in an interval and in a triangle
• An Iterative Procedure with Interface Relaxation for Domain Decomposition Methods
• From Electrostatics to Almost Optimal Nodal Sets for Polynomial Interpolation in a Simplex

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