CORDIS Project
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The project focuses on developing a new numerical method for solving fully nonlinear partial differential equations, particularly Hamilton-Jacobi-Bellman equations. It aims to enhance finite element methods with adaptive mesh refinement to improve accuracy in various applications, including finance and physics.
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 loc…
FRIEDRICH-SCHILLER-UNIVERSITÄT JENA
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