A probabilistic finite element method based on random meshes: A posteriori error estimators and Bayesian inverse problems

We 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 mesh FEM (RM-FEM). Our methodology allows to introduce probability measure standard piecewise linear FEM. posteriori error estimators uniquely information. A series numerical experiments illustrates potential RM-FEM estimation validates our analysis. furthermore demonstrate how employing enhances quality Bayesian inverse problems, thus allowing better errors in pipelines computations.