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Bibliographic Details
Main Authors: Bazon, Pedro B., Gebhardt, Cristian G., Buscaglia, Gustavo C., Ausas, Roberto F.
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2506.10894
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Table of Contents:
  • We investigate an optimization problem that arises when working within the paradigm of Data-Driven Computational Mechanics. In the context of the diffusion-reaction problem, such an optimization problem seeks for the continuous primal fields (gradient and flux) that are closest to some predefined discrete fields taken from a material data set. The optimization is performed over primal fields that satisfy the physical conservation law and the geometrical compatibility. We consider a reaction term in the conservation law, which has the effect of coupling all the optimality conditions. We first establish the well-posedness in the continuous setting. Then, we propose stable finite element discretizations that consistently approximate the continuous formulation, preserving its saddle-point structure and allowing for equal-order interpolation of all fields. Finally, we demonstrate the effectiveness of the proposed methods through a set of numerical examples.