Alena Dvořáková

Alena Dvořáková completed her doctoral work at the Faculty of Electrical Engineering, Mathematics and Computer Science at Delft University of Technology, where her dissertation developed a posteriori error analysis for finite element discretisations of degenerate parabolic equations arising in porous media flow and nonlinear diffusion. The work established sharp residual-based error bounds and an adaptive refinement strategy that preserved monotonicity under mesh coarsening — a stability property absent from standard isotropic refinement procedures. She subsequently held a postdoctoral fellowship at the Weierstrass Institute for Applied Analysis and Stochastics in Berlin, where she extended these methods to free boundary problems and moving interface equations with degenerate coefficients, collaborating with the numerical analysis group on finite element schemes for the Stefan problem and obstacle-type variational inequalities.

Following the postdoctoral position, Dvořáková developed monotone finite difference schemes for Hamilton-Jacobi equations on irregular computational grids, with a focus on the stability and convergence properties required for degenerate problems where classical consistency arguments break down. Her analysis of upwind-biased discretisations for convection-dominated diffusion problems produced computable stability constants applicable to a class of second-order degenerate operators that includes the Kolmogorov equations arising in stochastic analysis. This line of work bridged classical numerical PDE theory and the computational demands of optimal control, establishing rigorous foundations for schemes used in practice without formal convergence guarantees.

At IADU, Dvořáková provides the numerical analysis rigour underlying the Institute's computational programme in stochastic control and HJB methods. Her work examines the convergence and stability of finite difference and finite element approximations to degenerate parabolic equations in the Hamilton-Jacobi-Bellman and Fokker-Planck settings, with particular attention to the interaction between scheme monotonicity and the viscosity solution framework. She contributes to the development of provably convergent discretisation strategies for mean field game systems and supports the verification of numerical methods used across IADU's quantitative research output.