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This paper considers the asymptotic behaviour of a practical numerical approximation of the Navier–Stokes equations in ष, a bounded subdomain of 2 . The scheme consists of a conforming finite element spatial discretization, combined with an order-preserving linearly implicit implementation of...
The quadratic matrix equation AX 2 + BX + C = 0in n × nmatrices arises in applications and is of intrinsic interest as one of the simplest nonlinear matrix equations. We give a complete characterization of solutions in terms of the generalized Schur decomposition and describe and compare various...
The aim of this paper is to propose a stabilization technique in order to circumvent the two inf–sup conditions needed for stability of the discretization of the three fields formulation for domain decomposition methods (following the work of Brezzi & Marini (1993) Optimisation et Controle...
In this paper we describe a fully discrete quadrature method for the numerical solution of a hypersingular integral equation of the first kind for the scattering of time-harmonic elastic waves by a cavity crack. We establish convergence of the method and prove error estimates in a Hölder space...
We consider a Galerkin finite element method that uses piecewise bilinears on a modified Shishkin mesh for a model singularly perturbed convection–diffusion problem on the unit square. The method is shown to be convergent, uniformly in the perturbation parameter ॉ, of order N −1 in a global...
The classical Kantorovich theorem on Newton’s method assumes that the derivative of the operator involved satisfies a Lipschitz condition ‖F′(x) − F′(y)‖ ≤ L‖x − y‖. In this paper we weaken this condition, assuming that ‖F′(x) − F′(x 0 )‖ ≤ L‖x − x 0 ‖for a...
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