Rate-optimal goal-oriented adaptive FEM for semilinear elliptic PDEs

DOI10.1016/j.camwa.2022.05.008OpenAlexW4281388473WikidataQ114201458 ScholiaQ114201458MaRDI QIDQ2147328

Michael Innerberger, Jens Markus Melenk, Maximilian Brunner, Dirk Praetorius, Roland Becker

Publication date: 23 June 2022

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2022.05.008

zbMATH Keywords

adaptive finite element methodoptimal convergence ratesa posteriori error estimationquantity of interestsemilinear PDEsgoal-oriented adaptive algorithm

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Error bounds for boundary value problems involving PDEs (65N15) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50)

Related Items (4)

Cost-optimal adaptive iterative linearized FEM for semilinear elliptic PDEs ⋮ Goal-oriented error estimation based on equilibrated flux and potential reconstruction for the approximation of elliptic and parabolic problems ⋮ Plain convergence of goal-oriented adaptive FEM ⋮ Goal-oriented error analysis of iterative Galerkin discretizations for nonlinear problems including linearization and algebraic errors

Uses Software

• MooAFEM

Cites Work

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