# Error estimates for the Ultra Weak Variational Formulation of the Helmholtz equation

ESAIM: Mathematical Modelling and Numerical Analysis (2008)

- Volume: 42, Issue: 6, page 925-940
- ISSN: 0764-583X

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topBuffa, Annalisa, and Monk, Peter. "Error estimates for the Ultra Weak Variational Formulation of the Helmholtz equation." ESAIM: Mathematical Modelling and Numerical Analysis 42.6 (2008): 925-940. <http://eudml.org/doc/250381>.

@article{Buffa2008,

abstract = {
The Ultra Weak Variational Formulation (UWVF) of the Helmholtz equation
provides a variational framework suitable for discretization using plane wave solutions
of an appropriate adjoint equation. Currently convergence of the method is only proved
on the boundary of the domain. However substantial computational evidence
exists showing that the method also converges throughout the domain of the Helmholtz equation. In this paper we exploit the fact that the UWVF is essentially an upwind discontinuous Galerkin method to prove convergence of the solution in the special case where there is no absorbing medium present. We also provide some other estimates in the case when absorption is present, and give some simple numerical results to test the estimates. We expect that similar techniques can be used to prove error estimates for the UWVF
applied to Maxwell's equations and elasticity.
},

author = {Buffa, Annalisa, Monk, Peter},

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

keywords = {Helmholtz equation; UWVF; plane waves; error estimate.; error estimate; ultra weak variational formulation; convergence; discontinuous Galerkin method; numerical results; Maxwell's equations; elasticity},

language = {eng},

month = {8},

number = {6},

pages = {925-940},

publisher = {EDP Sciences},

title = {Error estimates for the Ultra Weak Variational Formulation of the Helmholtz equation},

url = {http://eudml.org/doc/250381},

volume = {42},

year = {2008},

}

TY - JOUR

AU - Buffa, Annalisa

AU - Monk, Peter

TI - Error estimates for the Ultra Weak Variational Formulation of the Helmholtz equation

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2008/8//

PB - EDP Sciences

VL - 42

IS - 6

SP - 925

EP - 940

AB -
The Ultra Weak Variational Formulation (UWVF) of the Helmholtz equation
provides a variational framework suitable for discretization using plane wave solutions
of an appropriate adjoint equation. Currently convergence of the method is only proved
on the boundary of the domain. However substantial computational evidence
exists showing that the method also converges throughout the domain of the Helmholtz equation. In this paper we exploit the fact that the UWVF is essentially an upwind discontinuous Galerkin method to prove convergence of the solution in the special case where there is no absorbing medium present. We also provide some other estimates in the case when absorption is present, and give some simple numerical results to test the estimates. We expect that similar techniques can be used to prove error estimates for the UWVF
applied to Maxwell's equations and elasticity.

LA - eng

KW - Helmholtz equation; UWVF; plane waves; error estimate.; error estimate; ultra weak variational formulation; convergence; discontinuous Galerkin method; numerical results; Maxwell's equations; elasticity

UR - http://eudml.org/doc/250381

ER -

## References

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## Citations in EuDML Documents

top- Christian Wieners, Barbara Wohlmuth, Robust operator estimates and the application to substructuring methods for first-order systems
- Teemu Luostari, Tomi Huttunen, Peter Monk, Error estimates for the ultra weak variational formulation in linear elasticity
- Teemu Luostari, Tomi Huttunen, Peter Monk, Error estimates for the ultra weak variational formulation in linear elasticity
- Claude J. Gittelson, Ralf Hiptmair, Ilaria Perugia, Plane wave discontinuous Galerkin methods: Analysis of the -version

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