arXiv subjects

Koffi Wilfrid Houedanou

Publications and source records attributed to Koffi Wilfrid Houedanou.

3 recordsLinked to original sources

arXiv2019

Residual-based a posteriori error estimates for a conforming mixed finite element discretization of the Monge-Ampère equation

In this paper we develop a new a posteriori error analysis for the Monge-Ampère equation approximated by conforming finite element method on isotropic meshes in 2D. The approach utilizes a slight variant of the mixed discretization proposed by Gerard Awanou and Hengguang Li in International Journal of Numerical Analysis and Modeling, 11(4):745-761, 2014. The a posteriori error estimate is based on a suitable evaluation on the residual of the finite element solution. It is proven that the a posteriori error estimate provided in this paper is both reliable and efficient.

math.NA↗

arXiv2017

An a posteriori error analysis for a coupled continuum pipe-flow/Darcy model in Karst aquifers: anisotropic and isotropic discretizations

This paper presents an a posteriori error analysis for a coupled continuum pipe-flow/Darcy model in karst aquifers. We consider a unified anisotropic finite element discretization (i.e. elements with very large aspect ratio). Our analysis covers two-dimensional domains, conforming and nonconforming discretizations as well as different elements. Many examples of finite elements that are covered by analysis are presented. From the finite element solution, the error estimators are constructed and based on the residual of model equations. Lower and upper error bounds form the main result with minimal assumptions on the elements. The lower error bound is uniform with respect to the mesh anisotropy in the entire domain. The upper error bound depends on a proper alignment of the anisotropy of the mesh which is a common feature of anisotropic error estimation. In the special case of isotropic meshes, the results simplify, and upper and lower error bounds hold unconditionally.

math.NA↗

arXiv2017

Residual-based a posteriori error estimates for a conforming finite element discretization of the Navier-Stokes/Darcy coupled problem

We consider in this paper, a new a posteriori residual type error estimator of a conforming mixed finite element method for the coupling of fluid flow with porous media flow on isotropic meshes. Flows are governed by the Navier-Stokes and Darcy equations, respectively, and the corresponding transmission conditions are given by mass conservation, balance of normal forces, and the Beavers-Joseph-Saffman law. The finite element subspaces consider Bernardi-Raugel and Raviart-Thomas elements for the velocities, piecewise constants for the pressures, and continuous piecewise linear elements for a Lagrange multiplier defined on the interface. The posteriori error estimate is based on a suitable evaluation on the residual of the finite element solution. It is proven that the a posteriori error estimate provided in this paper is both reliable and efficient. In addition, our analysis can be extended to other finite element subspaces yielding a stable Galerkin scheme.

math.NA↗