SIAM Journal on Numerical Analysis
Convergence Analysis of Orthogonal Spline Collocation for Elliptic Boundary Value Problems
SIAM Journal on Numerical Analysis
Finite Element Method for Elliptic Problems
Finite Element Method for Elliptic Problems
TH-Collocation for the biharmonic equation
Advances in Engineering Software
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In recent years, new and more effective procedures for applying collocation have been published. This article is devoted to present a revision of this subject and complement its developments. From the general theory two broad approaches are derived, which yield the direct and the indirect TH-collocation methods. The former approach had not been published before, and it is a dual of the indirect approach. In particular, second order differential equations of elliptic type are considered and several orthogonal collocation algorithms are developed for them. In TH-collocation, the approximations on the internal boundary and in the subdomain interiors are completely independent. This yields clear computational advantages that are illustrated through the construction of such algorithms. In the implementations presented, three dimensional problems are included. In passing, single-point-collocation methods that have been the subject of several recent publications are revised.