Numerical modelling of elliptic problems on octree-based meshes

We consider problems governed by a linear elliptic equation with varying coefficients across internal interfaces. The gradient of the solution can undergo significant variations through these internal boundaries. We present a compact finite-difference scheme on a tree-based adaptive grid that can be efficiently solved using a natively parallel data structure.Numerical illustrations are presented in two and three-dimensional configurations. Future perspectives will include the use of Hybrid High-Order methods to increase the approximation order. Contact: luca.formaggia@polimi.it