A mixed method for Dirichlet problems with radial basis functions

2013/02/08 by Norbert Heuer, Thanh Tran, Heuer, Norbert +1
Computer Science · Engineering · #65N12 #65N15 #65N30 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering

paper · pdf · doi:10.48550/arxiv.1302.2079

openalex publication_date 2013/02/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We present a simple discretization by radial basis functions for the Poisson equation with Dirichlet boundary condition. A Lagrangian multiplier using piecewise polynomials is used to accommodate the boundary condition. This simplifies previous attempts to use radial basis functions in the interior domain to approximate the solution and on the boundary to approximate the multiplier, which technically requires that the mesh norm in the interior domain is significantly smaller than that on the boundary. Numerical experiments confirm theoretical results.

Citations

• The finite element method with Lagrangian multipliers

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