6533b833fe1ef96bd129b74e

RESEARCH PRODUCT

Guaranteed and computable error bounds for approximations constructed by an iterative decoupling of the Biot problem

Svetlana KyasJan Martin NordbottenKundan KumarSergey Repin

subject

DiscretizationPoromechanics010103 numerical & computational mathematicsContraction mappings01 natural sciencesFOS: MathematicsDecoupling (probability)Applied mathematicsMathematics - Numerical Analysis0101 mathematicsvirheanalyysiMathematicsa posteriori error estimatesosittaisdifferentiaaliyhtälötA posteriori error estimatesfixed-stress split iterative schemeBiot numberNumerical Analysis (math.NA)Biot problem010101 applied mathematicsComputational MathematicsBiot problem; Fixed-stress split iterative scheme; A posteriori error estimates; Contraction mappingsComputational Theory and MathematicsElliptic partial differential equationModeling and SimulationNorm (mathematics)contraction mappingsA priori and a posterioriFixed-stress split iterative schemenumeerinen analyysiapproksimointiError detection and correction

description

The paper is concerned with guaranteed a posteriori error estimates for a class of evolutionary problems related to poroelastic media governed by the quasi-static linear Biot equations. The system is decoupled by employing the fixed-stress split scheme, which leads to an iteratively solved semi-discrete system. The error bounds are derived by combining a posteriori estimates for contractive mappings with functional type error control for elliptic partial differential equations. The estimates are applicable to any approximation in the admissible functional space and are independent of the discretization method. They are fully computable, do not contain mesh-dependent constants, and provide reliable global estimates of the error measured in the energy norm. Moreover, they suggest efficient error indicators for the distribution of local errors and can be used in adaptive procedures.

yearjournalcountryeditionlanguage
2021-06-01
http://arxiv.org/abs/1808.08036