# Direct and Inverse Problems for PDEs with Random Coefficients - Abstract

**Djurdjevac, Ana**

*Monte Carlo evolving surface finite element methods for PDEs with random coefficients on moving hypersurfaces*

We consider the analysis and numerical analysis of convection-diffusion equations with random coefficients on moving hypersurfaces. Under suitable regularity assumptions we prove existence and uniqueness of weak solutions. For discretization in space we apply the evolving surface finite element method to the weak form of the equation, for which we approximate the hypersurface by an evolving interpolated polyhedral surface. In order to deal with uncertainty, we use Monte Carlo method which approximates the expected value and we derive the error estimate for this approximation.