Quadratic B-splines on criss-cross triangulations for solving elliptic diffusion-type problems

In this paper we propose a method for the solution of elliptic diffusion-type problems based on bivariate quadratic B-splines on criss-cross triangulations. This technique considers the weak form of the differential problem and the Galerkin method to approximate the solution. As finite-dimensional space, we choose the space of quadratic splines on a criss-cross triangulation and we use its local basis both for the reconstruction of the physical domain and for the representation of the solution. Beside the theoretical description, we provide some numerical examples.