Goal-oriented adaptivity for a conforming residual minimization method in a dual discontinuous Galerkin norm

Type of publication
Article de presse
Auteurs

Sergio Rojas, David Pardo, Pouria Behnoudfar, Victor M. Calo

Abstract

We propose a goal-oriented mesh-adaptive algorithm for a finite element method stabilized via residual minimization on dual discontinuous-Galerkin norms. By solving a saddle-point problem, this residual minimization delivers a stable continuous approximation to the solution on each mesh instance and a residual projection onto a broken polynomial space, which is a robust error estimator to minimize the discrete energy norm via automatic mesh refinement. In this work, we propose and analyze a goal-oriented adaptive algorithm for this stable residual minimization. We solve the primal and adjoint problems considering the same saddle-point formulation and different right-hand sides. By solving a third stable problem, we obtain two efficient error estimates to guide goal-oriented adaptivity. We illustrate the performance of this goal-oriented adaptive strategy on advection–diffusion–reaction problems.

Conférence / Magazine
Computer Methods in Applied Mechanics and Engineering
Éditeur
Elsevier
Année de publication
2021
Citation bibliographique

Sergio Rojas, David Pardo, Pouria Behnoudfar, Victor M. Calo,
Goal-oriented adaptivity for a conforming residual minimization method in a dual discontinuous Galerkin norm,
Computer Methods in Applied Mechanics and Engineering,
Volume 377,
2021,
113686,
ISSN 0045-7825,
https://doi.org/10.1016/j.cma.2021.113686

DOI
https://doi.org/10.1016/j.cma.2021.113686