Article
| Title: | On the Maxwell-wave equation coupling problem and its explicit finite-element solution (English) |
| Author: | Beilina, Larisa |
| Author: | Ruas, Vitoriano |
| Language: | English |
| Journal: | Applications of Mathematics |
| ISSN: | 0862-7940 (print) |
| ISSN: | 1572-9109 (online) |
| Volume: | 68 |
| Issue: | 1 |
| Year: | 2023 |
| Pages: | 75-98 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | It is well known that in the case of constant dielectric permittivity and magnetic permeability, the electric field solving the Maxwell's equations is also a solution to the wave equation. The converse is also true under certain conditions. Here we study an intermediate situation in which the magnetic permeability is constant and a region with variable dielectric permittivity is surrounded by a region with a constant one, in which the unknown field satisfies the wave equation. In this case, such a field will be the solution of Maxwell's equation in the whole domain, as long as proper conditions are prescribed on its boundary. We show that an explicit finite-element scheme can be used to solve the resulting Maxwell-wave equation coupling problem in an inexpensive and reliable way. Optimal convergence in natural norms under reasonable assumptions holds for such a scheme, which is certified by numerical exemplification. (English) |
| Keyword: | constant magnetic permeability |
| Keyword: | dielectric permittivity |
| Keyword: | explicit scheme |
| Keyword: | finite element |
| Keyword: | mass lumping |
| Keyword: | Maxwell-wave equation |
| MSC: | 65M12 |
| MSC: | 65M22 |
| MSC: | 65M60 |
| idZBL: | Zbl 07655740 |
| idMR: | MR4541076 |
| DOI: | 10.21136/AM.2022.0210-21 |
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| Date available: | 2023-02-03T11:03:34Z |
| Last updated: | 2023-09-13 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/151497 |
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