Full discretization scheme for linearized quasi-static Maxwell's equations with a non-linear boundary condition
- Author
- Viera Zemanova (UGent) and Marian Slodicka (UGent)
- Organization
- Abstract
- We study a time dependent eddy current equation for the magnetic field H accompanied with a non-linear degenerate boundary condition, which is a generalization of the classical Silver-Muller condition for a non-perfect conductor. More exactly, the relation between the normal components of electric-E and magnetic-H fields obeys the following power law v x E = v x (vertical bar H x v vertical bar(alpha-1) H x v) for some alpha epsilon (0, 1]. We design a linear fully discrete approximation scheme to solve this nonlinear degenerate problem. The convergence of the approximations to a weak solation is proved, error estimates describing the dependance of the error on discretization parameters are derived as well.
- Keywords
- time- and space- discretization, linearized scheme, convergence, error estimates, non-linear Silver-Muller boundary condition, quasi-static Maxwell equations
Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-668660
- MLA
- Zemanova, Viera, and Marian Slodicka. “Full Discretization Scheme for Linearized Quasi-Static Maxwell’s Equations with a Non-Linear Boundary Condition.” AIP CONFERENCE PROCEEDINGS, vol. 1048, American Institute of Physics, 2008, pp. 621–24.
- APA
- Zemanova, V., & Slodicka, M. (2008). Full discretization scheme for linearized quasi-static Maxwell’s equations with a non-linear boundary condition. AIP CONFERENCE PROCEEDINGS, 1048, 621–624. Melville, NY, USA: American Institute of Physics.
- Chicago author-date
- Zemanova, Viera, and Marian Slodicka. 2008. “Full Discretization Scheme for Linearized Quasi-Static Maxwell’s Equations with a Non-Linear Boundary Condition.” In AIP CONFERENCE PROCEEDINGS, 1048:621–24. Melville, NY, USA: American Institute of Physics.
- Chicago author-date (all authors)
- Zemanova, Viera, and Marian Slodicka. 2008. “Full Discretization Scheme for Linearized Quasi-Static Maxwell’s Equations with a Non-Linear Boundary Condition.” In AIP CONFERENCE PROCEEDINGS, 1048:621–624. Melville, NY, USA: American Institute of Physics.
- Vancouver
- 1.Zemanova V, Slodicka M. Full discretization scheme for linearized quasi-static Maxwell’s equations with a non-linear boundary condition. In: AIP CONFERENCE PROCEEDINGS. Melville, NY, USA: American Institute of Physics; 2008. p. 621–4.
- IEEE
- [1]V. Zemanova and M. Slodicka, “Full discretization scheme for linearized quasi-static Maxwell’s equations with a non-linear boundary condition,” in AIP CONFERENCE PROCEEDINGS, Psalidi, GREECE, 2008, vol. 1048, pp. 621–624.
@inproceedings{668660,
abstract = {{We study a time dependent eddy current equation for the magnetic field H accompanied with a non-linear degenerate boundary condition, which is a generalization of the classical Silver-Muller condition for a non-perfect conductor. More exactly, the relation between the normal components of electric-E and magnetic-H fields obeys the following power law v x E = v x (vertical bar H x v vertical bar(alpha-1) H x v) for some alpha epsilon (0, 1]. We design a linear fully discrete approximation scheme to solve this nonlinear degenerate problem. The convergence of the approximations to a weak solation is proved, error estimates describing the dependance of the error on discretization parameters are derived as well.}},
author = {{Zemanova, Viera and Slodicka, Marian}},
booktitle = {{AIP CONFERENCE PROCEEDINGS}},
isbn = {{978-0-7354-0576-9}},
issn = {{0094-243X}},
keywords = {{time- and space- discretization,linearized scheme,convergence,error estimates,non-linear Silver-Muller boundary condition,quasi-static Maxwell equations}},
language = {{eng}},
location = {{Psalidi, GREECE}},
pages = {{621--624}},
publisher = {{American Institute of Physics}},
title = {{Full discretization scheme for linearized quasi-static Maxwell's equations with a non-linear boundary condition}},
volume = {{1048}},
year = {{2008}},
}