Work

Multigoal-oriented adaptive finite element methods with convergence rates

Year: 2026

Type: article

Abstract: We formulate and analyze a goal-oriented adaptive finite element method for a symmetric linear elliptic partial differential equation that can simultaneously deal with $$2 \le N$$ 2 ≤ N linear goal functionals. In each adaptive step, the proposed algorithm requires only to solve two linear finite element systems. Moreover, all finite element solutions are computed with respect to the same discrete space, while the underlying triangulations are adapted to resolve all inherent singularities simultaneously. Unlike available results for multigoal-oriented adaptive finite element methods in the literature, we give the first thorough convergence analysis and prove that our algorithm guarantees, in the usual sense, even optimal convergence rates. Numerical experiments underline the derived theoretical results.

Source: Numerische Mathematik

DOI: 10.1007/s00211-026-01576-w

Authors: Roland Becker, Maximilian Brunner, Paula Hilbert, Michael Innerberger, Dirk Praetorius

Institutions: Université de Pau et des Pays de l'Adour, Laboratoire de Mathématiques et de leurs Applications, TU Wien, Howard Hughes Medical Institute, Janelia Research Campus

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funders: Howard Hughes Medical Institute, Austrian Science Fund, Technische Universität Wien