Chen, Z. J.; Ewing, R. E. Local mesh refinement for degenerate two-phase incompressible flow problems. (English) Zbl 0943.65113 Bainov, D. (ed.), Proceedings of the 9th international colloquium on differential equations, Plovdiv, Bulgaria, August 18-23, 1998. Utrecht: VSP. 85-90 (1999). The authors develop finite element methods for degenerate elliptic-parabolic system which describes the flow of two incompressible, immiscible fluids in porous media \(\Omega \subset\mathbb{R}^d\), \(d\leq 3\): \[ -\nabla \cdot \left\{ k (\lambda(s) \nabla p + \gamma_1^\prime(s))\right\}= q(s), \tag{1} \]\[ \phi \partial_t s - \nabla \cdot \left\{k(\nabla \theta + \lambda_w(s)\nabla p + \gamma_2^\prime(s)) \right\}= q_w(s), \tag{2} \] where \(\phi\) and \(k\) are the porosity and absolute permeability of the porous system, \(s\) is the saturation of the wetting phase. Local mesh refinement techniques for solving of (1), (2) are discussed.For the entire collection see [Zbl 0914.00066]. Reviewer: Drumi Bainov (Sofia) MSC: 65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs Keywords:porous medium; degenerate elliptic-parabolic system; finite element; local mesh refinement PDFBibTeX XMLCite \textit{Z. J. Chen} and \textit{R. E. Ewing}, in: Proceedings of the 9th international colloquium on differential equations, Plovdiv, Bulgaria, August 18--23, 1998. Utrecht: VSP. 85--90 (1999; Zbl 0943.65113)