An Extended Error Analysis for a Meshfree Discretization Method of Darcy's Problem | Zendy

Daniela Schräder | Zendy; Holger Wendland | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Open Access

An Extended Error Analysis for a Meshfree Discretization Method of Darcy's Problem

Author(s) -

Daniela Schräder,

Holger Wendland

Publication year - 2012

Publication title -

siam journal on numerical analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.78

H-Index - 134

eISSN - 1095-7170

pISSN - 0036-1429

DOI - 10.1137/100806461

Subject(s) - smoothness , mathematics , discretization , radial basis function , basis function , collocation (remote sensing) , collocation method , mathematical analysis , meshfree methods , basis (linear algebra) , error analysis , finite element method , geometry , differential equation , computer science , ordinary differential equation , physics , machine learning , artificial neural network , thermodynamics

Recently [D. Schräder and H. Wendland, Math. Comp., 80 (2011), pp. 263–277], a new meshfree approximation method for Darcy’s problem has been introduced and analyzed. Thismethod is based on a symmetric collocation approach using radial basis functions producing solutions with an analytically divergence-free velocity part. However, the error analysis provided in that paper works only for smooth solutions, where the smoothness is intrinsically linked to the smoothness ofthe employed basis function. In this paper, we will extend the error analysis to less smooth functions, showing that the approximation order for rougher solutions is determined by the smoothness of the solution rather than the smoothness of the basis function

The content you want is available to Zendy users.

Already have an account? Click here to sign in.

Having issues? You can contact us here

Accelerating Research