Mixed and hybrid finite element methods
Mixed and hybrid finite element methods
A characteristics-mixed finite element method for advection-dominated transport problems
SIAM Journal on Numerical Analysis
Mixed finite element methods for nonlinear second-order elliptic problems
SIAM Journal on Numerical Analysis
Analysis of an Upwind-Mixed Finite Element Method for Nonlinear contaminant Transport Equations
SIAM Journal on Numerical Analysis
On Some Mixed Finite Element Methods with Numerical Integration
SIAM Journal on Scientific Computing
Mixed finite elements for the Richards' equation: linearization procedure
Journal of Computational and Applied Mathematics - Special issue: Selected papers from the 2nd international conference on advanced computational methods in engineering (ACOMEN2002) Liege University, Belgium, 27-31 May 2002
SIAM Journal on Numerical Analysis
Equivalent formulations and numerical schemes for a class of pseudo-parabolic equations
Journal of Computational and Applied Mathematics
Hi-index | 7.29 |
We present a mass conservative numerical scheme for reactive solute transport in porous media. The transport is modeled by a convection-diffusion-reaction equation, including equilibrium sorption. The scheme is based on the mixed finite element method (MFEM), more precisely the lowest-order Raviart-Thomas elements and one-step Euler implicit. The underlying fluid flow is described by the Richards equation, a possibly degenerate parabolic equation, which is also discretized by MFEM. This work is a continuation of Radu et al. (2008) and Radu et al. (2009) [1,2] where the algorithmic aspects of the scheme and the analysis of the discretization method are presented, respectively. Here we consider the Newton method for solving the fully discrete nonlinear systems arising on each time step after discretization. The convergence of the scheme is analyzed. In the case when the solute undergoes equilibrium sorption (of Freundlich type), the problem becomes degenerate and a regularization step is necessary. We derive sufficient conditions for the quadratic convergence of the Newton scheme.