# L2-stability of the upwind first order finite volume scheme for the Maxwell equations in two and three dimensions on arbitrary unstructured meshes

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

- Volume: 34, Issue: 1, page 139-158
- ISSN: 0764-583X

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topPiperno, Serge. "L2-stability of the upwind first order finite volume scheme for the Maxwell equations in two and three dimensions on arbitrary unstructured meshes." ESAIM: Mathematical Modelling and Numerical Analysis 34.1 (2010): 139-158. <http://eudml.org/doc/197507>.

@article{Piperno2010,

abstract = {
We investigate sufficient and possibly
necessary conditions for the L2 stability of the upwind first order
finite volume scheme for Maxwell equations, with metallic and
absorbing boundary conditions. We yield a very general sufficient condition,
valid for any finite volume partition in two and three space
dimensions. We show this condition is necessary for a class of
regular meshes in two space dimensions. However, numerical tests show
it is not necessary
in three space dimensions even on regular meshes. Stability limits for
time and space schemes with higher orders of accuracy are numerically
investigated.
},

author = {Piperno, Serge},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Electromagnetism; finite volume methods; L2
stability; energy methods; unstructured meshes; absorbing boundary
condition; metallic boundary condition.; stability; finite volume scheme; Maxwell's equations; absorbing boundary conditions},

language = {eng},

month = {3},

number = {1},

pages = {139-158},

publisher = {EDP Sciences},

title = {L2-stability of the upwind first order finite volume scheme for the Maxwell equations in two and three dimensions on arbitrary unstructured meshes},

url = {http://eudml.org/doc/197507},

volume = {34},

year = {2010},

}

TY - JOUR

AU - Piperno, Serge

TI - L2-stability of the upwind first order finite volume scheme for the Maxwell equations in two and three dimensions on arbitrary unstructured meshes

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2010/3//

PB - EDP Sciences

VL - 34

IS - 1

SP - 139

EP - 158

AB -
We investigate sufficient and possibly
necessary conditions for the L2 stability of the upwind first order
finite volume scheme for Maxwell equations, with metallic and
absorbing boundary conditions. We yield a very general sufficient condition,
valid for any finite volume partition in two and three space
dimensions. We show this condition is necessary for a class of
regular meshes in two space dimensions. However, numerical tests show
it is not necessary
in three space dimensions even on regular meshes. Stability limits for
time and space schemes with higher orders of accuracy are numerically
investigated.

LA - eng

KW - Electromagnetism; finite volume methods; L2
stability; energy methods; unstructured meshes; absorbing boundary
condition; metallic boundary condition.; stability; finite volume scheme; Maxwell's equations; absorbing boundary conditions

UR - http://eudml.org/doc/197507

ER -

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## Citations in EuDML Documents

top- Loula Fezoui, Stéphane Lanteri, Stéphanie Lohrengel, Serge Piperno, Convergence and stability of a discontinuous Galerkin time-domain method for the 3D heterogeneous Maxwell equations on unstructured meshes
- Loula Fezoui, Stéphane Lanteri, Stéphanie Lohrengel, Serge Piperno, Convergence and stability of a discontinuous Galerkin time-domain method for the 3D heterogeneous Maxwell equations on unstructured meshes

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