A mixed finite element method for Darcy flow in fractured porous media with non-matching grids

• Published in: ESAIM. Mathematical modelling and numerical analysis Vol. 46; no. 2; pp. 465 - 489
• Main Authors: D’Angelo, Carlo, Scotti, Anna
• Format: Journal Article
• Language: English
• Published: Les Ulis EDP Sciences 01.03.2012
• Subjects: 35Q86; 65L60; 76S05; Acceleration of convergence; Algebra; Algebraic geometry; Approximation; Boundary conditions; Computational fluid dynamics; Computer simulation; Darcy’s equation; embedded interface; Exact sciences and technology; extended finite element; fictitious domain; Finite element analysis; Finite element method; Fluid flow; Fluid mechanics; Fracture mechanics; fractured porous media; Mathematical analysis; Mathematical models; Mathematics; Media; mixed finite element; Numerical analysis; Numerical analysis. Scientific computation; Numerical linear algebra; Permeability; Porous materials; Sciences and techniques of general use; Simulation; Studies; unfitted mesh; Three-dimensional calculations; Triangle; Iterative method; Numerical method; Boundary condition; Implementation; Direct method; Finite element method; Convergence rate; Mixed finite element; Mathematical model; Numerical convergence; Numerical stability; Approximation; Grid pattern; Convergence acceleration; Numerical linear algebra; Raviart Thomas element; Incompressible flow; Numerical analysis; Linear system; Matrix inversion; Condition number; Two-dimensional calculations; Preconditioning

We consider an incompressible flow problem in a N-dimensional fractured porous domain (Darcy’s problem). The fracture is represented by a (N − 1)-dimensional interface, exchanging fluid with the surrounding media. In this paper we consider the lowest-order (ℝ T0, ℙ0) Raviart-Thomas mixed finite elem...