Analysis of discontinuous Galerkin methods using mesh-dependent norms and applications to problems with rough data

We prove the inf-sup stability of a discontinuous Galerkin scheme for second order elliptic operators in (unbalanced) mesh-dependent norms for quasi-uniform meshes for all spatial dimensions. This results in a priori error bounds in these norms. As an application we examine some problems with rough source term where the solution can not be characterised as a weak solution and show quasi-optimal error control

Listeria monocytogenes Internalin B Activates Junctional Endocytosis to Accelerate Intestinal Invasion

Listeria monocytogenes (Lm) uses InlA to invade the tips of the intestinal villi, a location at which cell extrusion generates a transient defect in epithelial polarity that exposes the receptor for InlA, E-cadherin, on the cell surface. As the dying cell is removed from the epithelium, the surrounding cells reorganize to form a multicellular junction (MCJ) that Lm exploits to find its basolateral receptor and invade. By examining individual infected villi using 3D-confocal imaging, we uncovered a novel role for the second major invasin, InlB, during invasion of the intestine. We infected mice intragastrically with isogenic strains of Lm that express or lack InlB and that have a modified InlA capable of binding murine E-cadherin and found that Lm lacking InlB invade the same number of villi but have decreased numbers of bacteria within each infected villus tip. We studied the mechanism of InlB action at the MCJs of polarized MDCK monolayers and find that InlB does not act as an adhesin, but instead accelerates bacterial internalization after attachment. InlB locally activates its receptor, c-Met, and increases endocytosis of junctional components, including E-cadherin. We show that MCJs are naturally more endocytic than other sites of the apical membrane, that endocytosis and Lm invasion of MCJs depends on functional dynamin, and that c-Met activation by soluble InlB or hepatocyte growth factor (HGF) increases MCJ endocytosis. Also, in vivo, InlB applied through the intestinal lumen increases endocytosis at the villus tips. Our findings demonstrate a two-step mechanism of synergy between Lm's invasins: InlA provides the specificity of Lm adhesion to MCJs at the villus tips and InlB locally activates c-Met to accelerate junctional endocytosis and bacterial invasion of the intestine

Lagrange multipliers in intrinsic elasticity

In an intrinsic approach to three-dimensional linearized elasticity, the unknown is the linearized strain tensor field (or equivalently the stress tensor field by means of the constitutive equation), instead of the displacement vector field in the classical approach. We consider here the pure traction problem and the pure displacement problem and we show that, in each case, the intrinsic approach leads to a quadratic minimization problem constrained by Donati-like relations (the form of which depends on the type of boundary conditions considered). Using the Babuška-Brezzi inf-sup condition, we then show that, in each case, the minimizer of the constrained minimization problem found in an intrinsic approach is the first argument of the saddle-point of an ad hoc Lagrangian, so that the second argument of this saddle-point is the Lagrange multiplier associated with the corresponding constraints. Such results have potential applications to the numerical analysis and simulation of the intrinsic approach to three-dimensional linearized elasticity

Finite Element Convergence For The Darwin Model To Maxwell's Equations

. We will derive the H(curl; \Omega\Gamma and H(curl; div;\Omega\Gamma variational formulations for the Darwin model of approximation to Maxwell's equations in three dimensions, and prove the well-posedness of the variational systems. Then Nedelec's and standard finite element methods are used to solve two kinds of variational problems. Though symmetric bilinear forms in the variational systems fail to define full norms equivalent to the standard norms in the finite element subspaces of H(curl; and H(curl; div;\Omega\Gammav we can still prove the finite element convergence and obtain the error estimates, without requiring the physical domains to be convex. 1. Introduction. It is known that there are more and more scientific problems which involve the solutions of Maxwell's equations, e.g., plasma physics, microwave devices, diffraction of electromagnetic waves. In many cases, the numerical resolution of the full system of Maxwell's equations may be very expensive in terms of the com..

Criticality Computation with Finite Element Method on Non-Conforming Meshes

International audienceIn this work, we proposed and study a method to use non-conforming meshing for core reactor simulation. This consists in a domain decomposition with Lagrange multipliers of the well known Raviart-Thomas finite element method. Here, we provide an a priori error estimate for criticality computation

Fully discrete finite element approaches for time-dependent Maxwell equations

A fully discrete finite element method is used to approximate the electric field equation derived from Maxwell equations in three dimensional polyhedral domains. Optimal energy-norm error estimates are achieved for general Lipschitz polyhedral domains. Optimal L 2 -norm error estimates are obtained for convex polyhedral domains. R'esum'e On r'esout, dans un domaine poly'edrique, les 'equations de Maxwell temporelles. Une m'ethode par 'el'ements finis discr`ete en temps et en espace est propos'ee pour calculer le champ 'electrique. Une estimation d'ordre optimal est obtenue pour l'erreur en norme-'energie dans le cas g'en'eral. Pour la norme L 2 , on obtient une estimation optimale dans le cas d'un poly`edre convexe. Mathematics Subject Classification (1991): 65N30, 35L15. A running title: Fully discrete schemes for Maxwell equations. Correspondence to: Jun Zou Department of Mathematics The Chinese University of Hong Kong Shatin, N.T. Hong Kong Email: [email protected] Fax: (8..