# A continuous finite element method with face penalty to approximate Friedrichs' systems

• Volume: 41, Issue: 1, page 55-76
• ISSN: 0764-583X

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## Abstract

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A continuous finite element method to approximate Friedrichs' systems is proposed and analyzed. Stability is achieved by penalizing the jumps across mesh interfaces of the normal derivative of some components of the discrete solution. The convergence analysis leads to optimal convergence rates in the graph norm and suboptimal of order ½ convergence rates in the L2-norm. A variant of the method specialized to Friedrichs' systems associated with elliptic PDE's in mixed form and reducing the number of nonzero entries in the stiffness matrix is also proposed and analyzed. Finally, numerical results are presented to illustrate the theoretical analysis.

## How to cite

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Burman, Erik, and Ern, Alexandre. "A continuous finite element method with face penalty to approximate Friedrichs' systems." ESAIM: Mathematical Modelling and Numerical Analysis 41.1 (2007): 55-76. <http://eudml.org/doc/250077>.

@article{Burman2007,
abstract = { A continuous finite element method to approximate Friedrichs' systems is proposed and analyzed. Stability is achieved by penalizing the jumps across mesh interfaces of the normal derivative of some components of the discrete solution. The convergence analysis leads to optimal convergence rates in the graph norm and suboptimal of order ½ convergence rates in the L2-norm. A variant of the method specialized to Friedrichs' systems associated with elliptic PDE's in mixed form and reducing the number of nonzero entries in the stiffness matrix is also proposed and analyzed. Finally, numerical results are presented to illustrate the theoretical analysis. },
author = {Burman, Erik, Ern, Alexandre},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Finite elements; interior penalty; stabilization methods; Friedrichs' systems; first-order PDE's.; finite elements; first-order PDEs; numerical results; convergence},
language = {eng},
month = {4},
number = {1},
pages = {55-76},
publisher = {EDP Sciences},
title = {A continuous finite element method with face penalty to approximate Friedrichs' systems},
url = {http://eudml.org/doc/250077},
volume = {41},
year = {2007},
}

TY - JOUR
AU - Burman, Erik
AU - Ern, Alexandre
TI - A continuous finite element method with face penalty to approximate Friedrichs' systems
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2007/4//
PB - EDP Sciences
VL - 41
IS - 1
SP - 55
EP - 76
AB - A continuous finite element method to approximate Friedrichs' systems is proposed and analyzed. Stability is achieved by penalizing the jumps across mesh interfaces of the normal derivative of some components of the discrete solution. The convergence analysis leads to optimal convergence rates in the graph norm and suboptimal of order ½ convergence rates in the L2-norm. A variant of the method specialized to Friedrichs' systems associated with elliptic PDE's in mixed form and reducing the number of nonzero entries in the stiffness matrix is also proposed and analyzed. Finally, numerical results are presented to illustrate the theoretical analysis.
LA - eng
KW - Finite elements; interior penalty; stabilization methods; Friedrichs' systems; first-order PDE's.; finite elements; first-order PDEs; numerical results; convergence
UR - http://eudml.org/doc/250077
ER -

## References

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