[كتاب][B] Robust numerical methods for singularly perturbed differential equations

HG Roos - 2008‏ - Springer
The analysis of singular perturbed differential equations began early in the twentieth
century, when approximate solutions were constructed from asymptotic expansions …

Stabilization of incompressibility and convection through orthogonal sub-scales in finite element methods

R Codina - Computer methods in applied mechanics and …, 2000‏ - Elsevier
Two apparently different forms of dealing with the numerical instability due to the
incompressibility constraint of the Stokes problem are analyzed in this paper. The first of …

[كتاب][B] Anisotropic finite elements: local estimates and applications

T Apel - 1999‏ - athene-forschung.rz.unibw …
The solution of elliptic boundary value problems may have anisotropic behaviour in parts of
the domain. That means that the solution varies signicantly only in certain directions …

[PDF][PDF] Variational multiscale methods in computational fluid dynamics

R Codina, S Badia, J Baiges, J Principe - … of computational mechanics, 2018‏ - deca.upc.edu
This article describes the Variational Multiscale Method (VMS) applied to flow problems. The
main idea of the formulation in the case of stationary linear problems is explained with some …

A low order Galerkin finite element method for the Navier–Stokes equations of steady incompressible flow: a stabilization issue and iterative methods

MA Olshanskii - Computer Methods in Applied Mechanics and …, 2002‏ - Elsevier
A Galerkin finite element method is considered to approximate the incompressible Navier–
Stokes equations together with iterative methods to solve a resulting system of algebraic …

Robust numerical methods for singularly perturbed differential equations: a survey covering 2008–2012

HG Roos - International Scholarly Research Notices, 2012‏ - Wiley Online Library
We present new results in the numerical analysis of singularly perturbed convection‐
diffusion‐reaction problems that have appeared in the last five years. Mainly discussing …

Crouzeix-Raviart type finite elements on anisotropic meshes

T Apel, S Nicaise, J Schöberl - Numerische Mathematik, 2001‏ - Springer
The paper deals with a non-conforming finite element method on a class of anisotropic
meshes. The Crouzeix-Raviart element is used on triangles and tetrahedra. For rectangles …

Anisotropic mesh adaptation in computational fluid dynamics: application to the advection–diffusion–reaction and the Stokes problems

L Formaggia, S Micheletti, S Perotto - Applied Numerical Mathematics, 2004‏ - Elsevier
In this work we develop an anisotropic a posteriori error analysis of the advection–diffusion–
reaction and the Stokes problems. This is the first step towards the study of more complex …

Layer‐adapted grids for singular perturbation problems

HG Roos - ZAMM‐Journal of Applied Mathematics and …, 1998‏ - Wiley Online Library
In the present paper a survey is given on the application of Shishkin grids to convection‐
diffusion problems with dominant convection, further some new results and open problems …

hp discontinuous Galerkin approximations for the Stokes problem

A Toselli - Mathematical Models and Methods in Applied …, 2002‏ - World Scientific
We propose and analyze a discontinuous Galerkin approximation for the Stokes problem.
The finite element triangulation employed is not required to be conforming and we use …