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Arnold, Douglas N.; Wendland, Wolfgang L.

The convergence of spline collocation for strongly elliptic equations on curves. (English) Zbl 0592.65077

Numer. Math. 47, 317-341 (1985).
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.
Reviewer: V.Drápalík

Cited in 1 Review
Cited in 67 Documents

MSC:

65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
65R20 Numerical methods for integral equations
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
34B05 Linear boundary value problems for ordinary differential equations
65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations

Keywords:

asymptotic error analysis; smoothly graded meshes; asymptotic convergence; optimal order; Fourier expansion; collocation
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\textit{D. N. Arnold} and \textit{W. L. Wendland}, Numer. Math. 47, 317--341 (1985; Zbl 0592.65077)
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References:

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