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Bio
My research interests are focusing on the design and analysis offinite 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.
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.
Research Interests
Papers共 248 篇Author StatisticsCo-AuthorSimilar Experts
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Foundations of Computational Mathematicspp.1-21, (2024)
CoRR (2024)
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CoRR (2024)
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CoRR (2024)
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SIAM JOURNAL ON NUMERICAL ANALYSISno. 2 (2024): 893-918
CoRR (2024)
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IMA JOURNAL OF NUMERICAL ANALYSISno. 2 (2024): 980-1002
CoRR (2024)
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CoRR (2024)
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