Arrarás Ventura, AndrésPortero Egea, Laura2020-11-112020-11-1120180096-300310.1016/j.amc.2017.07.042https://academica-e.unavarra.es/handle/2454/38632In 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.35 p.application/pdfeng© 2017 Elsevier Inc. This manuscript version is made available under the CC-BY-NC-ND 4.0Cell-centered finite differenceDomain decompositionHierarchical gridLagrange multiplierMixed finite elementParabolic probleminfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccessAcceso abierto / Sarbide irekia