ERC Starting Grant · 2020
Discretization and adaptive approximation of fully nonlinear equations
Fully nonlinear partial differential equations (PDE) arise in many applications ranging from physics to economy. They are different from PDEs in mechanics, and the PDE theory relies on the generalized solution concept of so-called viscosity solutions. Monotone finite difference methods (FDM) are provably convergent for approximating viscosity solutions, but are restricted to regular meshes and low-order approximations, thus having limitations in resolving realistic geometries or dealing with local mesh refinement. As viscosity solutions are lacking smoothness properties in general, adaptive approximations are desirable. In contrast to FDM, finite element methods (FEM) offer the possibility…
From the public funding record at EU CORDIS. Describes the funded project, not the reviews below.