| Mario Bukal |
Institute for Analysis and Scientific Computing |
Vienna University of Technology |
Wiedner Hauptstrasse 8-10 |
1040 Wien, Austria |
E-mail: mbukal[at]asc.tuwien.ac.at |
Hello and welcome to my homepage.
I'm a Ph.D. student at the Graduate School
"PDETech" at Vienna University of Technology
and
member of the research group of Prof. Ansgar Jüngel.
Research interests
Analysis and numerics for higher order nonlinear evolution equations
arising from quantum semiconductor modeling and lubrication theory. Entropy
entropy-dissipation techniques and optimal control of nonlinear partial differential equations.
Participation at the following projects:
- Partial differential equations in technical systems: modeling, simulation, and control ( >> )
- Quantum transport equations: kinetic, relativistic, and diffusive phenomena
- Entropy entropy-dissipation methods for nonlinear partial differential equations of
higher order ( >> )
Supervisor: Prof. Dr. A. Jüngel ( >> )
Advisor: Dr. D. Matthes ( >> )
Publications
Preprints
- M. Bukal, A. Jüngel, D. Matthes. A multidimensional nonlinear sixth-order quantum diffusion equation. Submitted for publication, 2011.
Published papers in scientific journals
- M. Bukal, A. Jüngel, D. Matthes. Entropies for radially symmetric higher-order nonlinear diffusion equations. Commun. Math. Sci. 9 (2010), 353-382.
Diploma Thesis
Supervisor: prof.dr.sc. M. Jurak ( >> )
Title: Error estimates for the finite volume element method for elliptic boundary value problems
Abstract:
The finite volume element method for the Dirichlet elliptic boundary value problem
has been considered. In analysis of the method, we treat the method as a perturbation of the Galerkin
finite element method. This approach enables us to derive the optimal error
estimates in H1 and L2 norm.
The method has been implemented in the mathematical tool FreeFem++ via
external functions. Using that tool we have shown theoretical results on one example,
while the counterexample reveals that the finite volume element method cannot have standard O(h2) convergence
rate in the L2 norm when the source term is only in L2 space.
Full text available in Croatian: Ocjena greske za metodu konacnih volumnih elemenata
Date of defense: April 9, 2008