Petrov-Galerkin spectral element method for mixed inhomogeneous boundary value problems on polygons

DOI10.1007/s11401-010-0614-3zbMath1218.65136OpenAlexW2022963516MaRDI QIDQ619648

Ben-yu Guo, Hong-Li Jia

Publication date: 25 January 2011

Published in: Chinese Annals of Mathematics. Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11401-010-0614-3

zbMATH Keywords

quadrilateralsLegendre quasi-orthogonal approximationmixed inhomogeneous boundary value problemsPetrov-Galerkin spectral element method

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Boundary value problems for second-order elliptic equations (35J25) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50)

Related Items (15)

Galerkin–Legendre spectral method for Neumann boundary value problems in three dimensions ⋮ Legendre spectral method for solving mixed boundary value problems on rectangle ⋮ A Petrov-Galerkin spectral method for fourth-order problems ⋮ A novel spectral method and error analysis for fourth-order equations in a spherical region ⋮ An efficient finite-element method and error analysis for the fourth-order elliptic equation in a circular domain ⋮ An efficient spectral method and rigorous error analysis based on dimension reduction scheme for fourth order problems ⋮ A triangular spectral element method for elliptic and Stokes problems ⋮ A spectral method for solving nonhomogeneous Neumann boundary value problems on quadrilaterals ⋮ A multi-domain spectral-Galerkin method for the Neumann problem on quadrilaterals ⋮ A novel spectral method and error estimates for fourth-order problems with mixed boundary conditions in a cylindrical domain ⋮ Pseudospectral method for quadrilaterals ⋮ Composite spectral method for exterior problems with polygonal obstacles ⋮ Some progress in spectral methods ⋮ A new Galerkin spectral element method for fourth-order boundary value problems ⋮ Spectral method for fourth-order problems on quadrilaterals

Cites Work

• Jacobi approximations in non-uniformly Jacobi-weighted Sobolev spaces
• Composite Laguerre-Legendre spectral method for exterior problems
• Jacobi approximations in certain Hilbert spaces and their applications to singular differential equations
• Optimal spectral-Galerkin methods using generalized Jacobi polynomials
• Composite generalized Laguerre-Legendre spectral method with domain decomposition and its application to Fokker-Planck equation in an infinite channel
• Spectral method on quadrilaterals
• Spectral Methods and Their Applications
• Spectral Methods
• Spectral Methods
• Spectral/hp Element Methods for Computational Fluid Dynamics
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