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:

  1. Partial differential equations in technical systems: modeling, simulation, and control ( >> )
  2. Quantum transport equations: kinetic, relativistic, and diffusive phenomena
  3. Entropy entropy-dissipation methods for nonlinear partial differential equations of higher order ( >> )

Supervisor: Prof. Dr. A. Jüngel ( >> )

Advisor: Dr. D. Matthes ( >> )

Publications

Preprints

  1. M. Bukal, A. Jüngel, D. Matthes. A multidimensional nonlinear sixth-order quantum diffusion equation. Submitted for publication, 2011.

Published papers in scientific journals

  1. 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