Volume 16, Issue 4
On Vector Helmholtz Equation with a Coupling Boundary Condition
DOI:

Numer. Math. J. Chinese Univ. (English Ser.)(English Ser.) 16 (2007), pp. 358-369

Published online: 2007-11

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• Abstract

The Helmholtz equation is sometimes supplemented by conditions that include the specification of the boundary value of the divergence of the unknown. In this paper, we study the vector Helmholtz problem in domains of both $C^{1,1}$ and Lipschitz. We establish a rigorous variational analysis such as equivalence, existence and uniqueness. And we propose finite element approximations based on the uncoupled solutions. Finally we present a convergence analysis and error estimates.

• Keywords

@Article{NM-16-358, author = {G. Li, J. S. Zhang, J. Zhu and D. P. Yang}, title = {On Vector Helmholtz Equation with a Coupling Boundary Condition}, journal = {Numerical Mathematics, a Journal of Chinese Uniersities}, year = {2007}, volume = {16}, number = {4}, pages = {358--369}, abstract = { The Helmholtz equation is sometimes supplemented by conditions that include the specification of the boundary value of the divergence of the unknown. In this paper, we study the vector Helmholtz problem in domains of both $C^{1,1}$ and Lipschitz. We establish a rigorous variational analysis such as equivalence, existence and uniqueness. And we propose finite element approximations based on the uncoupled solutions. Finally we present a convergence analysis and error estimates.}, issn = {}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/nm/10065.html} }
TY - JOUR T1 - On Vector Helmholtz Equation with a Coupling Boundary Condition AU - G. Li, J. S. Zhang, J. Zhu & D. P. Yang JO - Numerical Mathematics, a Journal of Chinese Uniersities VL - 4 SP - 358 EP - 369 PY - 2007 DA - 2007/11 SN - 16 DO - http://dor.org/ UR - https://global-sci.org/intro/nm/10065.html KW - AB - The Helmholtz equation is sometimes supplemented by conditions that include the specification of the boundary value of the divergence of the unknown. In this paper, we study the vector Helmholtz problem in domains of both $C^{1,1}$ and Lipschitz. We establish a rigorous variational analysis such as equivalence, existence and uniqueness. And we propose finite element approximations based on the uncoupled solutions. Finally we present a convergence analysis and error estimates.