in this research, the effect of surface roughness and bubble injection on skin friction and hydrodynamic drag force has been numerically considered. this research is based on taylor-couette flow. considered flow includes two concentric cylinders which internal cylinder is movable and external is immovable. the effective equations on the flow includes: equations of momentum, continuous, turbulen...

The primal hybrid method for solving second-order elliptic equations is extended from finite element approximations to general bases. Variational techniques are used to show convergence of approximations to the solution of the homogeneous Dirichlet problem for selfadjoint equations. Error estimates are obtained and examples are given. Introduction Lagrange multipliers have been employed to defi...

These notes describe some aspects of partial diierential equations from the view point of the variational calculus. We begin by showing how a vari-ational problem (the study of critical points of an action functional) can be associated to a diierential equation. Here the idea is to deene the action in such a way that the associated Euler-Lagrange equation is the diierential equation of interest...

This paper describes the use of matched asymptotic expansions to illuminate the description of functions exhibiting Stokes phenomenon. In particular the approach highlights the way in which the local structure and the possibility of finding Stokes multipliers explicitly depend on the behaviour of the coefficients of the relevant asymptotic expansions.

Recently, adaptive wavelet strategies for symmetric, positive definite operators have been introduced that were proven to converge. This paper is devoted to the generalization to saddle point problems which are also symmetric, but indeenite. Firstly, we derive explicit criteria for adaptively reened wavelet spaces in order to fullll the Ladyshenskaja{Babu ska{Brezzi (LBB) condition and to be fu...

Contents 1. Introduction 2 1.1. Porous media 2 1.2. Defining the microstructure 2 1.3. Darcy's law 3 2. Function spaces 4 2.1. Definitions 4 2.2. Some properties 5 3. Pressure as a Lagrange multiplier 5 3.1. A splitting of H 1 0 (Γ) 5 3.2. Finding the pressure 7 4. Solving the Stokes problem 7 5. Technical preliminaries for Darcy's law 9 5.1. The Poincaré inequality in Ω ε 9 5.2. Extension and ...

The weak Lagrange–Galerkin finite element method for the two-dimensional shallow water equations on adaptive unstructured grids is presented. The equations are written in conservation form and the domains are discretized using triangular elements. Lagrangian methods integrate the governing equations along the characteristic curves, thus being well suited for resolving the non-linearities introd...

We use a modification of the parameterization method to study invariant manifolds for difference equations. We establish existence, regularity, smooth dependence on parameters and study several singular limits, even if the difference equations do not define a dynamical system. This method also leads to efficient algorithms that we present with their implementations. The manifolds we consider in...

When space-time is assumed to be non-Riemannian the minimal coupling procedure (MCP) is not compatible, in general, with minimal action principle (MAP). This means that the equations gotten by applying MCP to the Euler-Lagrange equations of a Lagrangian L do not coincide with the Euler-Lagrange equations of the Lagrangian obtained by applying MCP to L. Such compatibility can be restored if the ...

This thesis is centred around higher-order invariant variational problems defined on Lie groups. We are mainly motivated by applications in computational anatomy and quantum control, but the general framework is relevant in many other contexts as well. We first develop a higher-order analog of Euler–Poincaré reduction theory for variational problems with symmetry and discuss the important examp...