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

Baranger, Jacques, and Machmoum, Ahmed. "A “Natural” Norm for the Method of Characteristics Using Discontinuous Finite Elements : 2D and 3D case." ESAIM: Mathematical Modelling and Numerical Analysis 33.6 (2010): 1223-1240. <http://eudml.org/doc/197515>.

@article{Baranger2010,
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. },
author = {Baranger, Jacques, Machmoum, Ahmed},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Method of characteristics; discontinuous finite elements; advection equation.; error estimates; first-order stationary hyperbolic equation; method of characteristics},
language = {eng},
month = {3},
number = {6},
pages = {1223-1240},
publisher = {EDP Sciences},
title = {A “Natural” Norm for the Method of Characteristics Using Discontinuous Finite Elements : 2D and 3D case},
url = {http://eudml.org/doc/197515},
volume = {33},
year = {2010},
}

TY - JOUR
AU - Baranger, Jacques
AU - Machmoum, Ahmed
TI - A “Natural” Norm for the Method of Characteristics Using Discontinuous Finite Elements : 2D and 3D case
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 33
IS - 6
SP - 1223
EP - 1240
AB - 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.
LA - eng
KW - Method of characteristics; discontinuous finite elements; advection equation.; error estimates; first-order stationary hyperbolic equation; method of characteristics
UR - http://eudml.org/doc/197515
ER -