On some convergence properties for finite element approximations to the inverse of linear elliptic operators
This paper deals with convergence theorems of the Galerkin finite element approximation for the second-order elliptic boundary value problems. Under some quite general settings, we show not only the pointwise convergence but also prove that the norm of approximate operator converges to the correspon...
Elmentve itt :
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| Dokumentumtípus: | Cikk |
| Megjelent: |
University of Szeged, Institute of Informatics
Szeged
2023
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| Sorozat: | Acta cybernetica
26 No. 1 |
| Kulcsszavak: | Differenciálegyenletek - részleges, Matematikai analízis, Galerkin módszer, Lineáris elliptikus operátor |
| Tárgyszavak: | |
| doi: | 10.14232/actacyb.294906 |
| Online Access: | http://acta.bibl.u-szeged.hu/86966 |
| Tartalmi kivonat: | This paper deals with convergence theorems of the Galerkin finite element approximation for the second-order elliptic boundary value problems. Under some quite general settings, we show not only the pointwise convergence but also prove that the norm of approximate operator converges to the corresponding norm for the inverse of a linear elliptic operator. Since the approximate norm estimates of linearized inverse operator play an essential role in the numerical verification method of solutions for non-linear elliptic problems, our result is also important in terms of guaranteeing its validity. Furthermore, the present method can also be applied to more general elliptic problems, e.g., biharmonic problems and so on. |
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| Terjedelem/Fizikai jellemzők: | 71-82 |
| ISSN: | 2676-993X |