Displaying similar documents to “Convergence of locally divergence-free discontinuous-Galerkin methods for the induction equations of the 2D-MHD system”

A “Natural” Norm for the Method of Characteristics Using Discontinuous Finite Elements : 2D and 3D case

Jacques Baranger, Ahmed Machmoum (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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We consider the numerical approximation of a first order stationary hyperbolic equation by the method of characteristics with pseudo time step using discontinuous finite elements on a mesh 𝒯 h . For this method, we exhibit a “natural” norm || || for which we show that the discrete variational problem P h k is well posed and we obtain an error estimate. We show that when goes to zero problem ( P h k ) (resp. the || || norm) has as a limit problem ( ) (resp. the || || norm) associated...

On the -stabilization of the double integrator subject to input saturation

Yacine Chitour (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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We consider a finite-dimensional control system ( Σ ) x ˙ ( t ) = f ( x ( t ) , u ( t ) ) , such that there exists a feedback stabilizer that renders x ˙ = f ( x , k ( x ) ) globally asymptotically stable. Moreover, for with an output map and 1 p q , we assume that there exists a 𝒦 -function such that H ( x u ) q α ( u p ) , where is the maximal solution of ( Σ ) k x ˙ ( t ) = f ( x ( t ) , k ( x ( t ) ) + u ( t ) ) , corresponding to and to the initial condition . Then, the gain function G ( H , p , q ) of given by 14.5cm G ( H , p , q ) ( X ) = def sup u p = X H ( x u ) q , is well-defined. We call profile of for any 𝒦 -function which is of the same order of magnitude...