Portero Egea, Laura

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https://academica-e.unavarra.es/handle/2454/49803

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Portero Egea

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Laura

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Estadística, Informática y Matemáticas

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InaMat2. Instituto de Investigación en Materiales Avanzados y Matemáticas

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0000-0002-7521-2097

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88600

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2608

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2018 - 20192
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Subject: Mixed finite element ×

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Now showing 1 - 2 of 2
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    PublicationOpen Access
    Multipoint flux mixed finite element methods for slightly compressible flow in porous media
    (Elsevier, 2019) Arrarás Ventura, Andrés; Portero Egea, Laura; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
    In this paper, we consider multipoint flux mixed finite element discretizations for slightly compressible Darcy flow in porous media. The methods are formulated on general meshes composed of triangles, quadrilaterals, tetrahedra or hexahedra. An inexact Newton method that allows for local velocity elimination is proposed for the solution of the nonlinear fully discrete scheme. We derive optimal error estimates for both the scalar and vector unknowns in the semidiscrete formulation. Numerical examples illustrate the convergence behavior of the methods, and their performance on test problems including permeability coefficients with increasing heterogeneity.
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    PublicationOpen Access
    Decoupling mixed finite elements on hierarchical triangular grids for parabolic problems
    (Elsevier, 2018) Arrarás Ventura, Andrés; Portero Egea, Laura; Ingeniería Matemática e Informática; Matematika eta Informatika Ingeniaritza
    In this paper, we propose a numerical method for the solution of time-dependent flow problems in mixed form. Such problems can be efficiently approximated on hierarchical grids, obtained from an unstructured coarse triangulation by using a regular refinement process inside each of the initial coarse elements. If these elements are considered as subdomains, we can formulate a non-overlapping domain decomposition method based on the lowest-order Raviart–Thomas elements, properly enhanced with Lagrange multipliers on the boundaries of each subdomain (excluding the Dirichlet edges). A suitable choice of mixed finite element spaces and quadrature rules yields a cell-centered scheme for the pressures with a local 10-point stencil. The resulting system of differential-algebraic equations is integrated in time by the Crank–Nicolson method, which is known to be a stiffly accurate scheme. As a result, we obtain independent subdomain linear systems that can be solved in parallel. The behavior of the algorithm is illustrated on a variety of numerical experiments.