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math.NA2026
Neural enrichment finite element method: A hybrid framework for problems with strong oscillations or interface problems
Shihan Guo, Thomas Richter
We propose a hybrid method, the Neural Enrichment Finite Element Method (NEFEM), designed for problems involving strong oscillations or interface problems with weak discontinuities…
math.NA2025
Dual Weighted Residual-driven adaptive mesh refinement to enhance biomechanical simulations
Roland Becker, Franz Chouly, Michel Duprez +3
This chapter describes how a posteriori error estimates targeting a user-defined quantity of interest, using the Dual Weighted Residual (DWR) technique, can be easily applied for b…
math.NA2024
A Posteriori Single- and Multi-Goal Error Control and Adaptivity for Partial Differential Equations
Bernhard Endtmayer, Ulrich Langer, Thomas Richter +2
This work reviews goal-oriented a posteriori error control, adaptivity and solver control for finite element approximations to boundary and initial-boundary value problems for stat…