PRIMUS Research Programme

Project title

Numerical analysis of non-smooth PDE

Description

This project aims to develop efficient and accurate numerical methods for the numerical solution of non-smooth Partial Differential Equations. We focus both on the situation where the problem itself is non-smooth (e.g. arising from the minimisation a non-differentiable energy functional), or where the solution of the problem is not assumed to have any additional smoothness than naturally suggested by the problem. Novel non-conforming discretisations and algorithms specifically tailored for non-smooth problems will be developed, and a corresponding convergence and priori error analysis under minimal smoothness assumptions will be carried out. Concerning a posteriori error analysis, we will design adaptive numerical methods based on rigorous a posteriori bounds, that substantially accelerate the current state-of-the-art methods. Particular attention will be placed on (but not restricted to) systems arising in fluid and solid mechanics.

Open positions

A fully funded position is available:

• PhD student (expected starting date: spring or fall semester 2026). Candidates for the PhD position should go through the application process for doctoral studies at the Faculty of Mathematics and Physics, usually in the spring to start in the fall semester, although a start in the spring semester is also possible. For details see: here

Ideally the candidate should have a strong background in the analysis of PDE and numerical analysis, including the finite element method. Programming skills are very desirable. The position includes funding to attend conferences and meetings. Before applying (and for informal queries), please contact Dr. Alexei Gazca via email (gazca@karlin.mff.cuni.cz)