My research interests are in numerical analysis. My work so far has consisted in building numerical methods, together with efficient solvers, for degenerate elliptic partial differential equations using monotone schemes. On the theory side, I am also interested in viscosity solutions which are the prevalent framework and correct notion of weak solution to prove convergence of monotone schemes.
|Address:||Department of Mathematics,|
|University of Michigan,|
|530 Church Street,|
|Ann Arbor, MI 48109|
|Office:||3831 East Hall|
We introduce generalised finite difference methods for solving fully nonlinear elliptic partial differential equations. Methods are based on piecewise Cartesian meshes augmented by additional points along the boundary. This allows for adaptive meshes and complicated geometries, while still ensuring consistency, monotonicity, and convergence. We describe an algorithm for efficiently computing the non-traditional finite difference stencils. We also present a strategy for computing formally higher-order convergent methods. Computational examples demonstrate the efficiency, accuracy, and flexibility of the methods.Read More »