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A “Natural” Norm for the Method of Characteristics Using Discontinuous Finite Elements : 2D and 3D case
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- Journal:
- ESAIM: Mathematical Modelling and Numerical Analysis / Volume 33 / Issue 6 / November 1999
- Published online by Cambridge University Press:
- 15 August 2002, pp. 1223-1240
- Print publication:
- November 1999
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- Article
- Export citation
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We consider the numerical approximation of a first orderstationary 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 weobtain 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 (P h ) (resp. the || ||h norm) associated to the Galerkin discontinuousmethod. This extends to two and three space dimension our previous results obtained in one space dimension.
