NumPDEs : Work group on Numerics of PDEs
My research is concerned with the numerical analysis of partial differential equations (PDEs), with a particular focus on finite element methods (FEMs). My scientific interests range from theoretical questions in numerical mathematics (e.g., a posteriori error analysis, convergence and optimality of adaptive finite element schemes) and uncertainty quantification (stochastic Galerkin FEM for PDEs with parametric or random input) to the design and analysis of effective approximation methods for (nonlinear) PDEs in materials science and engineering (e.g., in micromagnetics and liquid crystal theory).
Lecture:The mathematics of liquid crystals. Summer Semester 2021. TU Wien.
Conference:9th International Conference on Computational Methods in Applied Mathematics (CMAM 2022). August 29 - September 2, 2022. TU Wien.
Conference:13th International Symposium on Hysteresis Modeling and Micromagnetics (HMM 2023). May/June 2023 (precise dates to be fixed soon). TU Wien.
- April 9, 2021.The paperConvergence and rate optimality of adaptive multilevel stochastic Galerkin FEM, that I wrote together with Dirk Praetorius and Alex Bespalov, has been accepted for publication in IMA Journal of Numerical Analysis.
- March 26, 2021.A new preprint is available at arXiv:2103.13926. Together with Ricardo H. Nochetto and Shuo Yang, we propose a novel finite element method for the Ericksen model of nematic liquid crystals.
- March 17, 2021.Today, in the frame of the PDE Aternoon, the weekly meeting organized by our SFB and DK, I am giving an overview talk about our latest results on adaptive stochastic Galerkin FEM.