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

Jacques Baranger; Ahmed Machmoum

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

- Volume: 33, Issue: 6, page 1223-1240
- ISSN: 0764-583X

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topBaranger, 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 -

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