AN EXTENDED ERROR ANALYSIS FOR A MESHFREE DISCRETIZATION METHOD OF DARCY'S PROBLEM

作者：Schraeder Daniela; Wendland Holger

来源：SIAM Journal on Numerical Analysis, 2012, 50(2): 838-857.

DOI：10.1137/100806461

• partial differential equations
• radial basis functions
• high-order method
• collocation
• error analysis

Recently [D. Schrader and H. Wendland, Math. Comp., 80 (2011), pp. 263-277], a new meshfree approximation method for Darcy's problem has been introduced and analyzed. This method 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 of the 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.

• 出版日期2012