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Decoupling mixed finite elements on hierarchical triangular grids for parabolic problems

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  • Arrarás, A.
  • Portero, L.

Abstract

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.

Suggested Citation

  • Arrarás, A. & Portero, L., 2018. "Decoupling mixed finite elements on hierarchical triangular grids for parabolic problems," Applied Mathematics and Computation, Elsevier, vol. 319(C), pages 662-680.
    • Handle: RePEc:eee:apmaco:v:319:y:2018:i:c:p:662-680
    DOI: 10.1016/j.amc.2017.07.042
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