Spline Spaces on TR-Meshes with Hanging Vertices

Piecewise polynomial spline spaces defined on mixed meshes consisting of triangles and rectangles are useful tools in the numerical solution of boundary value problems by the finite element method. Meshes with hanging vertices are especially convenient, since simplified refinement algorithms can be used. Despite these applications, there does not seem to be a constructive theory of such splines. Here we treat the C⁰ case. In addition to dimension formulae, the construction of explicit basis functions and their supports and stability are discussed, and the approximation power of the spaces is also treated. Splines on T-meshes are included as a special case.

Event Topic:

Computational Mathematics & Statistics