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— The paper is devoted to a gênerai finite element approximation ofthe solution of the Stokes équations for an incompressible viscous fluid, Both conforming and nonconforming finite element methods… (More)

- Michel Crouzeix
- 2007

Abstract We prove an inequality related to polynomial functions of a square matrix, involving the numerical range of the matrix. We also show extensions valid for bounded and also unbounded operators… (More)

On etablit la stabilite de la L 2 -projection sur quelques espaces a elements finis V h , consideree comme une application dans L p et W p 1 , 1≤p≤∞, sous des hypotheses de regularite faibles

- Michel Crouzeix, Bernard Philippe, Miloud Sadkane
- SIAM J. Scientific Computing
- 1994

This paper deals with the Davidson method that computes a few of the extreme eigenvalues of a symmetric matrix and corresponding eigenvectors. A general convergence result for methods based on… (More)

It is shown that the numerical range of a linear operator operator in a Hilbert space is a (complete) $(1{+}\sqrt2)$-spectral set. The proof relies, among other things, in the behavior of the Cauchy… (More)

- Georgios Akrivis, Michel Crouzeix, Charalambos Makridakis
- Math. Comput.
- 1998

We approximate the solution of initial boundary value problems for nonlinear parabolic equations. In space we discretize by finite element methods. The discretization in time is based on linear… (More)

- Georgios Akrivis, Michel Crouzeix, Charalambos Makridakis
- Numerische Mathematik
- 1999

Summary. Efficient combinations of implicit and explicit multistep methods for nonlinear parabolic equations were recently studied in [1]. In this note we present a refined analysis to allow more… (More)

- Michel Crouzeix, J. Rappaz
- 1990

This volume presents a general theory for the approximation of regular and bifurcation branches of solutions of nonlinear equations. After recalling basic results of nonlinear approximation theory,… (More)

It is shown thatA-acceptable and, more generally,A(θ)-arational approximations of bounded analytic semigroups in Banach space are stable. The result applies, in particular, to the Crank-Nicolson… (More)

- Georgios Akrivis, Michel Crouzeix
- Math. Comput.
- 2003

We construct and analyze combinations of rational implicit and explicit multistep methods for nonlinear parabolic equations. The resulting schemes are linearly implicit and include as particular… (More)