A computational tool for comparing all linear PDE solvers

DOI10.1007/s10444-014-9360-5zbMath1317.65228OpenAlexW1978312138MaRDI QIDQ2348692

Robert Schaback

Publication date: 15 June 2015

Published in: Advances in Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10444-014-9360-5

zbMATH Keywords

Sobolev spacesfinite elementserror boundsradial basis functionsfinite differenceskernelsmeshless methodsPetrov-Galerkin techniquessymmetric meshless collocation

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) Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite difference methods for boundary value problems involving PDEs (65N06) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22)

Related Items (16)

Numerical solution of sigularly perturbed parabolic problems by a local kernel-based method with an adaptive algorithm ⋮ Nonuniform sampling and approximation in Sobolev space from perturbation of the framelet system ⋮ Error Analysis of Nodal Meshless Methods ⋮ Local multilevel scattered data interpolation ⋮ Variable shape parameter strategy in local radial basis functions collocation method for solving the 2D nonlinear coupled Burgers' equations ⋮ Pseudospectral meshless radial point interpolation for generalized biharmonic equation in the presence of Cahn-Hilliard conditions ⋮ Small errors imply large evaluation instabilities ⋮ $H^2$-Convergence of Least-Squares Kernel Collocation Methods ⋮ On meshfree numerical differentiation ⋮ Greedy sparse linear approximations of functionals from nodal data ⋮ A meshless technique based on the radial basis functions for solving systems of partial differential equations ⋮ An approximation theorist's view on solving operator equations -- with special attention to Trefftz, MFS, MPS, and DRM methods ⋮ A local reproducing kernel method accompanied by some different edge improvement techniques: application to the Burgers' equation ⋮ All well-posed problems have uniformly stable and convergent discretizations ⋮ A greedy meshless local Petrov-Galerkin methodbased on radial basis functions ⋮ Local variably scaled Newton basis functions collocation method for solving Burgers' equation

Uses Software

• Matlab

Cites Work

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