| Title:
|
An adaptive finite element method in reconstruction of coefficients in Maxwell's equations from limited observations (English) |
| Author:
|
Beilina, Larisa |
| Author:
|
Hosseinzadegan, Samar |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
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61 |
| Issue:
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3 |
| Year:
|
2016 |
| Pages:
|
253-286 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We propose an adaptive finite element method for the solution of a coefficient inverse problem of simultaneous reconstruction of the dielectric permittivity and magnetic permeability functions in the Maxwell's system using limited boundary observations of the electric field in 3D. We derive a posteriori error estimates in the Tikhonov functional to be minimized and in the regularized solution of this functional, as well as formulate the corresponding adaptive algorithm. Our numerical experiments justify the efficiency of our a posteriori estimates and show significant improvement of the reconstructions obtained on locally adaptively refined meshes. (English) |
| Keyword:
|
Maxwell's system |
| Keyword:
|
coefficient inverse problem |
| Keyword:
|
Tikhonov functional |
| Keyword:
|
Lagrangian approach |
| Keyword:
|
a posteriori error estimate |
| MSC:
|
65M06 |
| MSC:
|
65M22 |
| MSC:
|
65M32 |
| MSC:
|
65M60 |
| MSC:
|
65N30 |
| idZBL:
|
Zbl 06587852 |
| idMR:
|
MR3502111 |
| DOI:
|
10.1007/s10492-016-0131-0 |
| . |
| Date available:
|
2016-05-19T08:51:23Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/145701 |
| . |
| Reference:
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