Jens Markus Melenk

Prof. Jens Markus Melenk is a Professor at TU Wien's Faculty of Mathematics and Geoinformation, leading the Computational Mathematics Research Group (E101-02-1). His research focuses on advanced numerical methods for partial differential equations, with a strong emphasis on hp-FEM (hp-Finite Element Method), fractional diffusion equations, and wave propagation problems. He has contributed significantly to the development of robust and efficient algorithms for complex domains and heterogeneous media.

Key research interests include the application of hp-FEM to fractional operators (e.g., integral fractional Laplacian), boundary element methods (BEM), and the analysis of wavenumber-explicit convergence for Maxwell's equations and elastic wave equations. His work bridges theoretical analysis and computational implementation, addressing challenges in multiscale problems and singular perturbations.

• Notable contributions: Exponential convergence of hp-FEM for fractional Laplacian problems, wavenumber-explicit error estimates for wave equations in heterogeneous media.
• Collaborations: Active involvement with researchers like Markus Faustmann, Christoph Schwab, and Dirk Praetorius.
• Supervised theses: Includes works on hp-FEM for fractional operators, RBF interpolation, and error estimators for elliptic PDEs.

His research group develops and analyzes numerical schemes for challenging PDE scenarios, with applications in electromagnetism, acoustics, and computational mechanics.