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Journal of Scientific Computing
Published in: Journal of Scientific Computing 3/2016

09-06-2016

An Adaptive Finite Element Method for the Transmission Eigenvalue Problem

Authors: Jiayu Han, Yidu Yang

Published in: Journal of Scientific Computing | Issue 3/2016

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Abstract

The classical weak formulation of the Helmholtz transmission eigenvalue problem can be linearized into an equivalent nonsymmetric eigenvalue problem. Based on this nonsymmetric eigenvalue problem, we first discuss the a posteriori error estimates and adaptive algorithm of conforming finite elements for the Helmholtz transmission eigenvalue problem. We give the a posteriori error indicators for primal eigenfunction, dual eigenfunction and eigenvalue. Theoretical analysis shows that the indicators for both primal eigenfunction and dual eigenfunction are reliable and efficient and that the indicator for eigenvalue is reliable. Numerical experiments confirm our theoretical analysis.
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Metadata
Title
An Adaptive Finite Element Method for the Transmission Eigenvalue Problem
Authors
Jiayu Han
Yidu Yang
Publication date
09-06-2016
Publisher
Springer US
Published in
Journal of Scientific Computing / Issue 3/2016
Print ISSN: 0885-7474
Electronic ISSN: 1573-7691
DOI
https://doi.org/10.1007/s10915-016-0234-5

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