|
Erik
Burman |
Chair of Mathematics Department of Mathematics University of Sussex Falmer, Brighton BN1 9RF United Kingdom phone:
+44 (0)1273 67 89 33 Office:
2A16 Office
hours: Thursdays 10-12 |
|
Full curriculum
vitae with publication list
Research interests:
My
main research interests are computational methods for complex flow problems. In
this framework I have investigated various aspects of stabilized finite element
methods, discontinuous Galerkin methods, a posteriori error estimation and
adaptive algorithms. Recent fields of interest include multiphysics coupling
(and decoupling) using NitscheÕs method, the stability properties of
discontinuous Galerkin methods for elliptic or hyperbolic problems, efficient
time stepping methods for hyperbolic systems and convection—diffusion
equations. Ongoing work focus on the solution and analysis of optimal control
and inverse problems using the above mentioned techniques.
Presentations:
Seminar on bubble stabilized
DG-methods (Magdeburg, INRIA, 2008)
Selected recent publications in reverse chronological
order:
E. Burman, A. Ern, M. Fern\`andez, Explicit Runge--Kutta schemes and finite elements
with symmetric stabilization for first-order linear PDE systems, submitted
to Siam Journal on Numerical Analysis.
E. Burman, M. Fern\`andez, Analysis of the PSPG method for the
transient Stokes' problem, submitted to Siam Journal on Numerical Analysis.
E. Burman, Consistent SUPG method for transient
transport problems: stability and convergence, to appear in Computer
Methods in Applied Mechanics and Engineering.
E. Burman, A
posteriori error estimation for interior penalty finite element approximations
of the advection--reaction equation, Siam Journal on Numerical Analysis,
Vol 47, No.5, pp. 3584-3607.
E. Burman and B. Stamm, Bubble stabilized discontinuous Galerkin
method for Stokes' problem, to appear in Math. Mod. and Meths. In App. Sci.
E. Burman, B. Stamm, Bubble stabilized discontinuous
Galerkin method for parabolic and elliptic problems, submitted to
Numerische Mathematik.
R. Becker, E. Burman and P. Hansbo, A Nitsche extended finite
element method for incompressible elasticity with discontinuous modulus of
elasticity, to appear in Computer Methods in Mechanics and Engineering.
E. Burman and M. Fernandez, Finite element methods with symmetric
stabilization for the transient convection--diffusion--reaction equation,
Computer Methods in Mechanics and Engineering 198 (2009), no. 33-36,
2508--2519.
E. Burman and M. Fern\`andez, Stabilization of explicit coupling in
fluid-structure interaction involving fluid incompressibility, Computer
Methods in Mechanics and Engineering 198 (2009), no. 5-8, 766--784.
E. Burman, J. Guzman, D. Leykekhman, Weighted error
estimates of the continuous interior penalty method for singularly perturbed
problems, IMA Journal of Numerical Analysis 29 (2009), no. 2, 284--314.
E. Burman and M. Fern\`andez, Galerkin finite element methods with symmetric
pressure stabilization for the transient Stokes' equations: stability and
convergence analysis, Siam Journal of Numerical Analysis 47 (2008/09), no.
1, 409--439.
E. Burman, B. Stamm, Low
order discontinuous Galerkin methods for second order elliptic problems,
Siam Journal on Numerical Analysis 47 (2008/09), no. 1, 508--533.
E. Burman, B. Stamm,
Minimal stabilization of discontinuous Galerkin finite element methods for
hyperbolic equations, Journal of Scientific Computing 33 (2007), no. 2,
183-208.
Teaching – spring term 2010
G5085 Analysis This link is no longer active please
contact David Seery (d.seery@sussex.ac.uk) for the address of the 2010
web-page.