2014
DOI: 10.1137/130907240
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Stabilized Finite Elements for a Reaction-Dispersion Saddle-Point Problem with NonConstant Coefficients

Abstract: We consider a system of two reaction-dispersion equations with nonconstant parameters. Both equations are coupled through the boundary conditions. We propose a mixed variational formulation that leads to a nonsymmetric saddle-point problem. We prove its well-posedness. Then, we develop a stabilized mixed finite element discretization of this problem and establish optimal a priori error estimates.

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Cited by 2 publications
(21 citation statements)
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“…We recall that this situation is already investigated in , Section 4] when the physical parameters are constant but seem close to real‐life values.…”
Section: Numerical Experimentsmentioning
confidence: 54%
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“…We recall that this situation is already investigated in , Section 4] when the physical parameters are constant but seem close to real‐life values.…”
Section: Numerical Experimentsmentioning
confidence: 54%
“…We recall that, according to the analysis of the abstract problem achieved in (see also ), necessary and sufficient conditions on the bilinear forms are required to ensure existence, uniqueness, and stability for the mixed problem . The inf‐sup conditions on the forms m (·,·) and m ∗ (·,·) easily follow from the imbedding of H01(normalΩ) into double-struckV, see , Lemmas and 2.3]. Lemma The bilinear form m (·,·) satisfies the inf‐sup condition for a positive constant η ψH01(normalΩ),2emsupφdouble-struckVm(ψ,φ)φdouble-struckV0.3emηψH1(normalΩ). The bilinear form m ∗ (·,·) satisfies the inf‐sup condition for a positive constant η ∗ ψH01(normalΩ),2emsupφdouble-struckVm(ψ,φ)φdouble-struckV0.3emηψH1(normalΩ). …”
Section: The Mixed Variational Frameworkmentioning
confidence: 99%
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