article · Computational Mathematics and Mathematical Physics
A new Finite Difference method called Discrete Duality Finite Difference method (DDFD method in short) to solve on quadrilateral meshes 2D-flow problems in homogeneous porous media with full diffusion matrix with constant coefficients is proposed and analyzed in the present work. We start with the derivation of the discrete problem. A result of existence and uniqueness of the solution for that problem is given via the positive definiteness of its associated matrix. Their theoretical p-roperties, namely, stability and error estimates (in discrete energy norm, L2-norm, relative L2-norm, $${{L}^{\infty }}$$ -norm), are investigated. Numerical tests are provided.
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DOI: 10.1134/s0965542524701173
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