A Legendre Spectral Collocation Method for the Biharmonic Dirichlet Problem

DOI10.1051/m2an:2000160zbMath0984.65121OpenAlexW2078752427MaRDI QIDQ4490028

Andreas Karageorghis, Bernard Bialecki

Publication date: 20 March 2002

Published in: ESAIM: Mathematical Modelling and Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/197522

zbMATH Keywords

numerical resultsSchur complementbiharmonic equationpreconditioned conjugate gradient methodbiharmonic Dirichlet problemLegendre spectral collocation method

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Boundary value problems for higher-order elliptic equations (35J40) Iterative numerical methods for linear systems (65F10) Numerical computation of matrix norms, conditioning, scaling (65F35) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22)

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Stokes eigenmodes in square domain and the stream function-vorticity correlation ⋮ Solution of the first biharmonic problem by the Trefftz method ⋮ Matrix decomposition algorithms for elliptic boundary value problems: A survey ⋮ A Legendre Petrov-Galerkin method for fourth-order differential equations ⋮ Exponentially accurate spectral element method for fourth order elliptic problems ⋮ A fast solver for the orthogonal spline collocation solution of the biharmonic Dirichlet problem on rectangles ⋮ Efficient spectral-Galerkin algorithms for direct solution of fourth-order differential equations using Jacobi polynomials ⋮ A Jacobi spectral Galerkin method for the integrated forms of fourth‐order elliptic differential equations

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