Rotation-Based Mixed Formulations for an Elasticity-Poroelasticity Interface Problem

Anaya, Verónica; Wijn, Zoa de; Gómez-Vargas, Bryan; Mora, David; Ruiz–Baier, Ricardo

doi:10.1137/19m1268343

Cited by 13 publications

(12 citation statements)

References 36 publications

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“…The expected O(h k+1 ) convergence is observed for all fields in their respective norms, accordingly to the theory from [4,3], and the effectivity index is close to constant for all mesh refinements. This same behaviour is seen even when the elastic or the poroelastic material is nearly incompressible (setting E = 10 5 , ν = 0.499) and when the poroelastic material it is nearly impermeable (setting κ = 10 −12 ), and we also note that the effectivity index is slightly modified, but it is still constant and not affected by the different parameter scaling, again confirming the robustness of the estimators.…”

Section: Computational Examplessupporting

confidence: 72%

“…The analysis of the continuous and discrete formulations is not found in [4,3]. For sake of completeness, we outline it in the Appendix.…”

Section: Discrete Spaces and Galerkin Formulationmentioning

confidence: 99%

“…We consider that the normal unit vector n on Σ points from Ω P to Ω E . The problem is stated as follows, which is as in [3], except for the particular scaling used herein…”

Section: Continuous Formulationmentioning

confidence: 99%

“…In the specific case of Biot poromechanics, this interaction occurs when the linearly elastic porous medium is saturated, and such problem is relevant to a large class of very diverse applications ranging from bone healing to, e.g., petroleum engineering, or sound isolation. We are also interested in the interface between elastic and poroelastic systems that are encountered in hydrocarbon production in deep subsurface reservoirs (a pay zone and the surrounding non-pay rock formation) [15], or in the study of tooth and periodontal ligament interactions [3].…”

mentioning

confidence: 99%

“…The schemes for elasticity and transmission elasticity-poroelasticity and their a priori error analysis have been studied in [4] and [3], respectively. The solvability of the rotation-based poroelasticity has not been addressed yet, and for sake of completeness we outline its analysis in Appendix A and Appendix B.…”

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confidence: 99%

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Robust a posteriori error analysis for rotation-based formulations of the elasticity/poroelasticity coupling

Anaya¹,

Khan²,

Mora³

et al. 2021

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We develop the a posteriori error analysis of three mixed finite element formulations for rotation-based equations in elasticity, poroelasticity, and interfacial elasticity-poroelasticity. The discretisations use H 1 -conforming finite elements of degree k + 1 for displacement and fluid pressure, and discontinuous piecewise polynomials of degree k for rotation vector, total pressure, and elastic pressure. Residual-based estimators are constructed, and upper and lower bounds (up to data oscillations) for all global estimators are rigorously derived. The methods are all robust with respect to the model parameters (in particular, the Lamé constants), they are valid in 2D and 3D, and also for arbitrary polynomial degree k ≥ 0. The error behaviour predicted by the theoretical analysis is then demonstrated numerically on a set of computational examples including different geometries on which we perform adaptive mesh refinement guided by the a posteriori error estimators.

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Section: Computational Examplessupporting

confidence: 72%

“…The analysis of the continuous and discrete formulations is not found in [4,3]. For sake of completeness, we outline it in the Appendix.…”

Section: Discrete Spaces and Galerkin Formulationmentioning

confidence: 99%

“…We consider that the normal unit vector n on Σ points from Ω P to Ω E . The problem is stated as follows, which is as in [3], except for the particular scaling used herein…”

Section: Continuous Formulationmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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