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

[4]	Xiaobing Feng, Thomas Lewis, and Stefan Schnake. Analysis of the Vanishing Moment Method and its Finite Element Approximations for Second-order Linear Elliptic PDEs in Non-divergence Form. Methods and Applications of Analysis, 2017 (submitted). [ arXiv ]
[3]	Xiaobing Feng and Stefan Schnake. A Discontinuous Ritz Method for a Class of Calculus of Variations Problems. International Journal of Numerical Analysis and Modeling, 16(3):340--356, 2019. [ http | arXiv ]
[2]	Xiaobing Feng and Stefan Schnake. An enhanced finite element method for a class of variational problems exhibiting the Lavrentiev gap phenomenon. Communications in Computational Physics, 24(2):576-592, 2018. [ http | arXiv ]
[1]	Xiaobing Feng, Michael Neilan, and Stefan Schnake. Interior penalty discontinuous galerkin methods for second order linear non-divergence form elliptic pdes. Journal of Scientific Computing, 74(3):1651--1676, Mar 2018. [ bib | DOI | http | arXiv ]

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.