Two-dimensional mesh embedding for B-spline methods
A technique is developed for achieving a two-dimensional mesh embedding with B-splines as basis function. An algorithm is provided for generating a spline basis, where the domain is partitioned into arbitrary rectangles. The spline basis automatically has the same high degree of continuity (\(C^{d-1}\), where \(d\) is the polynomial degree) at zonal boundaries as everywhere else. The basis functions are simply a suitable product of one-dimensional B-splines. Both integer and noninteger refinement ratios are allowed across the mesh blocks. The basis may be used to form differential operators using a Galerkin or collocation scheme. Test cases for linear scalar equations such as the Poisson and advection equation are presented. \(\copyright\) Academic Press.
scientific article; zbMATH DE number 1212301