The convergence of spline collocation for strongly elliptic equations on curves
This paper presents a unified asymptotic error analysis for even as well as for odd degree splines subordinate. Uniform or smoothly graded meshes are in consideration only. The asymptotic convergence of optimal order is proved. The crucial assumption for the generalized boundary integral and integro- differential operators is strong ellipticity. The analysis is based on Fourier expansion, it extends known results to variable coefficient equations. This paper contains the first convergence proof of midpoint collocation with piecewise constant functions.
scientific article; zbMATH DE number 3951943
scientific article