On the numerical solution of some semilinear elliptic problems. II. (English) Zbl 1072.65156
Summary: In part I [cf. K. Atkinson and W. Han, ETNA, Electron. Trans. Numer. Anal. 17, 206–217 (2004; Zbl 1065.65133)], a Galerkin method was proposed and analyzed for the numerical solution of a Dirichlet problem for a semi-linear elliptic boundary value problem of the form \(-\Delta U = F(\cdot,U)\). This was converted to a problem on a standard domain and then converted to an equivalent integral equation. Galerkin’s method was used to solve the integral equation, with the eigenfunctions of the Laplacian operator on the standard domain \(D\) as the basis functions. In this paper we consider the implementing of this scheme, and we illustrate it for some standard domains \(D\).
MSC:
| 65N38 | Boundary element methods for boundary value problems involving PDEs |
| 35J65 | Nonlinear boundary value problems for linear elliptic equations |
Keywords:
Galerkin method; numerical examples; Dirichlet problem; semi-linear elliptic boundary value problem; equivalent integral equation; eigenfunctions; basis functionsCitations:
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