Stefan Schnake

Research Areas:

• Applied and Computational Mathematics

Research Interests:

• Numerical solutions to linear and nonlinear partial differential equations.
• Numerical solutions of functional minimization problems.
• Conforming and nonconforming Finite Element methods.
• Interior Penalty, Discontinuous Galerkin methods.
• The Lavrentiev Gap Phenomenon.
• Second-order, linear, elliptic PDEs in non-divergence form.
• Hamilton-Jacobi-Bellman equations.

Applications

• Material Science: Nonlinear Elasticity and Microstucture Theory
• Mathematical Finance: Stochastic Optimal Control

Recent Publications

• X. Feng, M. Neilan and S. Schnake. Interior penalty discontinuous Galerkin methods for second order linear non-divergence form elliptic PDEs, arXiv:1605.xxxxv1 [math.NA].
• X. Feng, S. Schnake. An enhanced finite element method for a class of variational problems exhibiting the Lavrentiev gap phenomenon, (in preparation).

Discontinous Galerkin Finite Element Numeric Calculus MATLAB Toolbox

I have developed a MATLAB toolbox to implement the Discontinuous Galerkin Finite Element Differential Calculus found here. This software allows one to take a discrete derivative of functions that are classically, weakly, and distributionally differentiable in one or two dimensions.

The documentation is available here and the code is available here for you to test and use. Note: This code is used as-is. I assume no loss or liability for the use of this code.