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

Abstract : 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.
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https://hal.inria.fr/hal-02422851
Contributor : Jan Papež Connect in order to contact the contributor
Submitted on : Thursday, May 20, 2021 - 1:49:58 PM
Last modification on : Monday, May 16, 2022 - 6:16:44 PM

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Jan Papež, Martin Vohralík. Inexpensive guaranteed and efficient upper bounds on the algebraic error in finite element discretizations. Numerical Algorithms, Springer Verlag, 2022, 89, pp.371-407. ⟨10.1007/s11075-021-01118-5⟩. ⟨hal-02422851v4⟩

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