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

0550968 - MÚ 2023 RIV NL eng J - Journal Article
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
R&D Projects: GA ČR(CZ) GA20-01074S
Institutional support: RVO:67985840
Keywords : a posteriori error estimate * algebraic error * finite element method
OECD category: Pure mathematics
Impact factor: 2.1, year: 2022
Method of publishing: Limited access
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.
Permanent Link: http://hdl.handle.net/11104/0326249