A high-order approximation method for semilinear parabolic equations on spheres

DOI10.1090/S0025-5718-2012-02623-8zbMath1276.35108OpenAlexW2102483543MaRDI QIDQ4911902

Holger Wendland

Publication date: 20 March 2013

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-2012-02623-8

zbMATH Keywords

spherical basis functionslinearized Crank-Nicholson method

Mathematics Subject Classification ID

Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20) Semilinear parabolic equations (35K58)

Related Items (12)

Convergence estimates for stationary radial basis function interpolation and for semi-discrete collocation-schemes ⋮ The meshless kernel-based method of lines for parabolic equations ⋮ NEW RESULTS FOR PARABOLIC EQUATION ON THE SPHERE WITH CAPUTO–FABRIZIO OPERATOR ⋮ Convergence of non-stationary semi-discrete RBF schemes for the heat and wave equation ⋮ Notes on continuity result for conformable diffusion equation on the sphere: the linear case ⋮ A Kernel-Based Least-Squares Collocation Method for Surface Diffusion ⋮ Numerical Solutions of a Boundary Value Problem on the Sphere Using Radial Basis Functions ⋮ Solving partial differential equations on (evolving) surfaces with radial basis functions ⋮ A Nash-Hörmander iteration and boundary elements for the Molodensky problem ⋮ A high-order meshless Galerkin method for semilinear parabolic equations on spheres ⋮ A High-Order, Analytically Divergence-Free Approximation Method for the Time-Dependent Stokes Problem ⋮ Extrinsic Meshless Collocation Methods for PDEs on Manifolds

Uses Software

• Matlab

Cites Work

• Unnamed Item
• Radial basis functions: developments and applications to planetary scale flows
• Stabilization of RBF-generated finite difference methods for convective PDEs
• Continuous and discrete least-squares approximation by radial basis functions on spheres
• Meshless methods: An overview and recent developments
• Error bounds for solving pseudodifferential equations on spheres by collocation with zonal kernels
• Approximation of parabolic PDEs on spheres using spherical basis functions
• Composition in fractional Sobolev spaces.
• Direct and inverse Sobolev error estimates for scattered data interpolation via spherical basis functions
• Transport schemes on a sphere using radial basis functions
• Spherical harmonics
• A radial basis function method for the shallow water equations on a sphere
• On Galerkin Methods in Semilinear Parabolic Problems
• Scattered Data Interpolation on Spheres: Error Estimates and Locally Supported Basis Functions
• Galerkin Finite Element Methods for Parabolic Problems
• Scattered Data Approximation

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