Publication:
Decoupling mixed finite elements on hierarchical triangular grids for parabolic problems

Date

2018

Director

Publisher

Elsevier
Acceso abierto / Sarbide irekia
Artículo / Artikulua
Versión aceptada / Onetsi den bertsioa

Project identifier

MINECO//MTM2014-52859-P/ES/recolecta

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.

Description

Keywords

Cell-centered finite difference, Domain decomposition, Hierarchical grid, Lagrange multiplier, Mixed finite element, Parabolic problem

Department

Ingeniería Matemática e Informática / Matematika eta Informatika Ingeniaritza

Faculty/School

Degree

Doctorate program

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