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Prof Erik Burman
Department of Mathematics
Gower Street
Tel: 02076793306
Prof Erik Burman profile picture
  • Chair of Computational Mathematics
  • Dept of Mathematics
  • Faculty of Maths & Physical Sciences

  • 2013 Chair of Computational Mathematics UCL.
  • 2007-2013 Professor of Mathematics, University of Sussex.
  • 2002-2007 Senior researcher, Chair of Modelling and Scientific Computing, Ecole Polytechnique Federale de Lausanne, Switzerland.
  • 2000-2002, Research Assistant, Chair of Analysis and Numerical Simulation, Ecole Polytechnique Federale de Lausanne, Switzerland.
  • 1998-2000, Research Assistant at the Centre de Mathématiques Appliquées (CMAP), École Polytechnique, Palaiseau, France.
  • 1998 PhD, "Adaptive methods for compressible two-phase flows", Chalmers University of Technology, Sweden.

Research Summary

My research interests are focusing on the design and analysis of
finite element and finite difference methods for partial differential equations. 
The general methodology consists in using finite element methods in combination with adaptive algorithms based on a posteriori error estimation to compute accurate approximate solutions to the partial differential equation at hand in an efficient way. 

The applied problems that I have studied include compressible flows, two-phase flows, solidification problems, visco-elastic flows, reactive flows and combustion problems as well as incompressible flows in different flow regimes, including high Reynolds flow and multi-physics couplings such as fluid-structure interaction. The computational solution of these problems are important in many fields in science and engineering, for instance in biomedical flow problems.

My theoretical investigations include a priori error analysis for Galerkin finite element methods using continuous and discontinuous approximation spaces in the h and the p framework, a posteriori error estimation for nonlinear problems and singularly perturbed elliptic problems, new stabilised finite element methods in computational fluid dynamics, convergence proofs for the linearised and fully nonlinear Navier-Stokes equation in the high Reynolds number regime,
time-discretisation methods for computational fluid mechanics and XFEM or unfitted methods for computational continuum mechanics.

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