Convergence analysis of a Finite Difference method for 2D-flow problems with a uniform full permeability tensor
Jeutsa Aubin Kinfack1, Hubert Donfack2, Flavian Emmanuel Sapnken3,4, Jean Gaston Tamba3,4
1Higher Technical Teachers' Training College, University, Buea, Cameroon
2Faculty of Science, University of Bamenda, Bambili, Cameroon
3University Institute of Technology, University of Douala, Douala, Cameroon
4Higher Institute of Transport, Logistic and Commerce, University of Ebolowa, Ambam, Cameroon
Keywords: finite difference, diffusion problems, homogeneous porous media
Abstract
We present in this work a convergence analysis of a Finite Difference method for solving on quadrilateral meshes 2D-flow problems in homogeneous porous media with a full permeability tensor. We start with the derivation of the discrete problem by using our finite difference formula for a mixed derivative of second order. A result of existence and uniqueness of the solution for that problem is given via the positive definiteness of its associated matrix. Their theoretical properties, namely, stability on the one hand (with the associated discrete energy norm) and error estimates (with L2-norm, relative L2-norm and L∞-norm ) are investigated. Numerical simulations are shown.
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