A Multivariate Spline Based Collocation Method for Numerical Solution of Partial Differential Equations

DOI10.1137/22M1469602zbMath1497.65245arXiv2109.09698OpenAlexW3200491574WikidataQ114073936 ScholiaQ114073936MaRDI QIDQ5866593

Ming-Jun Lai, Jinsil Lee

Publication date: 22 September 2022

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2109.09698

zbMATH Keywords

collocation methodPoisson equationmultivariate splineselliptic PDE in nondivergence form

Mathematics Subject Classification ID

Numerical computation using splines (65D07) Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Second-order elliptic equations (35J15) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Strong solutions to PDEs (35D35)

Related Items (1)

Trivariate spline collocation methods for numerical solution to 3D Monge-Ampère equation

Uses Software

• SplinePak

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On convergence rate of the augmented Lagrangian algorithm for nonsymmetric saddle point problems
• Bivariate splines for fluid flows
• Functional analysis, Sobolev spaces and partial differential equations
• A bivariate spline method for second order elliptic equations in non-divergence form
• A new \(H^2\) regularity condition of the solution to Dirichlet problem of the Poisson equation and its applications
• Solving elliptic PDE's on domains with curved boundaries with an immersed penalized boundary method
• Trivariate \(C^{r}\) polynomial macroelements
• Discontinuous Galerkin Finite Element Approximation of Nondivergence Form Elliptic Equations with Cordès Coefficients
• Spline Functions
• Bivariate Splines of Various Degrees for Numerical Solution of Partial Differential Equations
• Spline Functions on Triangulations
• A primal-dual weak Galerkin finite element method for second order elliptic equations in non-divergence form
• An Adaptive Triangulation Method for Bivariate Spline Solutions of PDEs
• Sparse Solutions of Underdetermined Linear Systems and Their Applications

This page was built for publication: A Multivariate Spline Based Collocation Method for Numerical Solution of Partial Differential Equations