MATHICSE-GroupAbdulle, AssyrGaregnani, Giacomo2021-03-112021-03-112021-03-112021-03-1010.5075/epfl-MATHICSE-283834https://infoscience.epfl.ch/handle/20.500.14299/175890We present a novel probabilistic finite element method (FEM) for the solution and uncertainty quantification of elliptic partial differential equations based on random meshes, which we call random mesh FEM (RM-FEM). Our methodology allows to introduce a probability measure on standard piecewise linear FEM.We present a posteriori error estimators based uniquely on probabilistic information. A series of numerical experiments illustrates the potential of the RM-FEM for error estimation and validates our analysis. We furthermore demonstrate how employing the RM-FEM enhances the quality of the solution of Bayesian inverse problems, thus allowing a better quantification of numerical errors in pipelines of computations.Probabilistic methods for PDEsRandom meshesUncertainty quantificationA posteriori error estimatorsBayesian inverse problemstext::working paper