Edge stabilization for the generalized Stokes problem: A continuous interior penalty method
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We consider a differential system based on the coupling of the Navier-Stokes and Darcy equations for modeling the interaction between surface and porous media flows. We formulate the problem as an interface equation, we analyze the associated (nonlinear) S ...
The numerical analysis of a dynamic constrained optimization problem is presented. It consists of a global minimization problem that is coupled with a system of ordinary differential equations. The activation and the deactivation of inequality constraints ...
In this paper we propose a stabilized conforming finite volume element method for the Stokes equations. On stating the convergence of the method, optimal a priori error estimates in different norms are obtained by establishing the adequate connection betwe ...
Engineers rely on efficient simulations that provide them with reliable data in order to make proper engineering design decisions. The purpose of this thesis is to design adaptive numerical methods for multiscale problems in this spirit. We consider ellipt ...
We present a new second-order method, based on the MAC scheme on cartesian grids, for the numerical simulation of two-dimensional incompressible flows past obstacles. In this approach, the solid boundary is embedded in the cartesian computational mesh. Dis ...
A new numerical method is proposed to study two-phase flow and heat transfer for interlayer cooling of the new generation of multi-stacked computer chips. The fluid flow equations are developed in 3-dimensions based on the Arbitrary Lagrangian-Eulerian for ...
Among the efficient numerical methods based on atomistic models, the quasi-continuum (QC) method has attracted growing interest in recent years. The QC method was first developed for crystalline materials with Bravais lattice and was later extended to mult ...
In this article the Stokes equations are considered in a domain simulating a capillary bed system. The capillaries are supposed to be thin, parallel and periodic. An asymptotic approximation is constructed. The macroscopic pressure satisfies a Robin interf ...
The goal of this project is to numerically solve the Navier-Stokes equations by using different numerical methods with particular emphasis on solving the problem of the flow past a square cylinder. In particular, we use the finite element method based on P ...
The aim of this paper is to develop and analyze a one-parameter family of stabilized discontinuous finite volume element methods for the Stokes equations in two and three spatial dimensions. The proposed scheme is constructed using a baseline finite elemen ...