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Numer. Math. 47, 317-341 (1985) Numerische 9 Springer-Verlag1985

Summary: Numer. Math. 47, 317-341 (1985) Numerische
9 Springer-Verlag1985
The Convergence of Spline Collocation
for Strongly Elliptic Equations on Curves*
Dedicated to Prof. Dr. Dr. h.c. mult. Lothar Collatz
on the occasion of his 75th birthday
Douglas N. Arnold 1 and Wolfgang L. Wendland2
1 Department of Mathematics,Universityof Maryland,CollegePark, MD 20742,USA
2 FachbereichMathematik,TechnischeHochschule,D-6100Darmstadt, Federal Republicof Ger-
Summary. Most boundary element methods for two-dimensional boundary
value problems are based on point collocation on the boundary and the use
of splines as trial functions. Here we present a unified asymptotic error
analysis for even as well as for odd degree splines subordinate to uniform
or smoothly graded meshes and prove asymptotic convergence of optimal
order. The equations are collocated at the breakpoints for odd degree and
the internodal midpoints for even degree splines. The crucial assumption
for the generalized boundary integral and integro-differential operators is
strong ellipticity. Our analysis is based on simple Fourier expansions. In


Source: Arnold, Douglas N. - School of Mathematics, University of Minnesota


Collections: Mathematics