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A “Natural” Norm for the Method of Characteristics Using Discontinuous Finite Elements : 2D and 3D case
Published online by Cambridge University Press: 15 August 2002
Abstract
We consider the numerical approximation of a first order
stationary hyperbolic equation by the method of characteristics with
pseudo time step k using discontinuous finite elements on a mesh
${\cal T}_h$. For this method, we exhibit a “natural” norm || ||h,k
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 k goes to zero problem
$(P_h^k)$
(resp. the || ||h,k norm)
has as a limit problem (Ph) (resp. the
|| ||h norm) associated to the Galerkin
discontinuous
method. This extends to two and three space dimension our previous
results obtained in one
space dimension.
- Type
- Research Article
- Information
- ESAIM: Mathematical Modelling and Numerical Analysis , Volume 33 , Issue 6 , November 1999 , pp. 1223 - 1240
- Copyright
- © EDP Sciences, SMAI, 1999
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