Inexpensive guaranteed and efficient upper bounds on the algebraic error in finite element discretizations

0550968 - MÚ 2023 RIV NL eng J - Článek v odborném periodiku
Papež, Jan - Vohralík, M.
Inexpensive guaranteed and efficient upper bounds on the algebraic error in finite element discretizations.
Numerical Algorithms. Roč. 89, č. 1 (2022), s. 371-407. ISSN 1017-1398. E-ISSN 1572-9265
Grant CEP: GA ČR(CZ) GA20-01074S
Institucionální podpora: RVO:67985840
Klíčová slova: a posteriori error estimate * algebraic error * finite element method
Obor OECD: Pure mathematics
Impakt faktor: 2.1, rok: 2022
Způsob publikování: Omezený přístup
https://doi.org/10.1007/s11075-021-01118-5

We present new constructions of (approximate) H(div, Ω)-liftings of the algebraic residual leading to estimators of the algebraic error in h and p finite element discretizations of a model diffusion problem. The estimators provide guaranteed bounds without any uncomputable constants and they are globally efficient, similarly to some recent developments, but the cost of their construction is significantly reduced. We provide a set of numerical experiments to assess the performance of the new estimators.
Trvalý link: http://hdl.handle.net/11104/0326249