3 papers
math.NA2026
The Bayesian Finite Element Method in Inverse Problems: a Critical Comparison between Probabilistic Models for Discretization Error
Anne Poot, Iuri Rocha, Pierre Kerfriden +1
When using the finite element method (FEM) in inverse problems, its discretization error can produce parameter estimates that are inaccurate and overconfident. The Bayesian finite…
cs.CE2025
A predictor-corrector scheme for approximating signed distances using finite element methods
Amina El Bachari, Johann Rannou, Vladislav A. Yastrebov +2
In this article, we introduce a finite element method designed for the robust computation of approximate signed distance functions to arbitrary boundaries in two and three dimensio…
math.NA2025
Effects of Interpolation Error and Bias on the Random Mesh Finite Element Method for Inverse Problems
Anne Poot, Iuri Rocha, Pierre Kerfriden +1
Bayesian inverse problems are an important application for probabilistic solvers of partial differential equations: when fully resolving numerical error is computationally infeasib…