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 . For this method, we exhibit a “natural” norm || || for which we show that the discrete variational problem is well posed and we obtain an error estimate. We show that when goes to zero problem (resp. the || || norm) has as a limit problem ( ) (resp. the || || norm) associated...