×

The embedding method for linear partial differential equations in unbounded and multiply connected domains. (English) Zbl 1106.65101

Summary: The recently suggested embedding method to solve linear boundary value problems [cf. P. N. Shankar, Proc. R. Soc. London A 461, No. 2059, 2121–2133 (2005; Zbl 1153.65369)] is here extended to cover situations where the domain of interest is unbounded or multiply connected. The extension involve the use of complete sets of exterior and interior eigenfunctions on canonical domains. Applications to typical boundary value problems for Laplace’s equation, the Oseen equations and the biharmonic equation are given as examples.

MSC:

65N25 Numerical methods for eigenvalue problems for boundary value problems involving PDEs
35P10 Completeness of eigenfunctions and eigenfunction expansions in context of PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35J40 Boundary value problems for higher-order elliptic equations

Citations:

Zbl 1153.65369
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Filon L N G, The forces on a cylinder in a stream of viscous fluid,Proc. R. Soc. London,A113 (1926) 7–27 · JFM 52.0867.01
[2] Miyagi T, Oseen flow past a circular cylinder,J. Phys. Soc. Japan 37 (1974) 1699–1707
[3] Shankar P N, On handling non-homogeneous corner data in confined steady Stokes flow,Proc. R. Soc. London A460 (2004) 479–485 · Zbl 1041.76018
[4] Shankar P N, Eigenfunction expansions on arbitrary domains,Proc. R. Soc. London A461 (2005) 2121–2133 · Zbl 1153.65369
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.