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

ESAIM: Mathematical Modelling and Numerical Analysis (2007)

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

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topBurman, 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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## Citations in EuDML Documents

top- Erik Burman, Alexandre Ern, Implicit-explicit Runge–Kutta schemes and finite elements with symmetric stabilization for advection-diffusion equations
- Erik Burman, Alexandre Ern, Implicit-explicit Runge–Kutta schemes and finite elements with symmetric stabilization for advection-diffusion equations
- Erik Burman, Alexandre Ern, Implicit-explicit Runge–Kutta schemes and finite elements with symmetric stabilization for advection-diffusion equations

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