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The construction of weighted extended B-splines (web-splines), as recently introduced by the authors and J. Wipper for uniform knot sequences, is generalized to the nonuniform case. We show that web-splines form a stable basis for splines on arbitrary domains in Rm which provides optimal approximation power. Moreover, homogeneous boundary conditions, as encountered frequently in finite element applications, can be satisfied exactly by using an appropriate weight function. To illustrate the performance of the method, it is applied to a scattered data fitting problem and a finite element approximation of an elliptic boundary value problem. [Copyright &y& Elsevier]

We describe a new finite element method which uses weighted extended B-splines on a regular grid as basis functions for solving Dirichlet problems on bounded domains in arbitrary dimensions. This web-method does not require any grid generation and can be implemented very efficiently. It yields smooth, high order accurate approximations with relatively low dimensional subspaces. [ABSTRACT FROM AUTHOR]

Uniform stability is a key property of B-spline bases, but so far, sharp bounds on the condition number have been available only for degrees ≤ 2. Relying on computer algebra to perform the rather elaborate computations, we derive the lowest upper bound on the condition number of cubic B-splines and present a conjecture concerning the according value for the quartic case. [ABSTRACT FROM AUTHOR]