Name
Abstract | ||
|---|---|---|
We propose a new numerical method for the solution of Bernoulli's free boundary value problem for a harmonic function w in a doubly connected domain D in $$\\mathbb {R}^2$$R2 where an unknown free boundary $$\\varGamma _0$$Γ0 is determined by prescribed Cauchy data of w on $$\\varGamma _0$$Γ0 in addition to a Dirichlet condition on the known boundary $$\\varGamma _1$$Γ1. Our method is based on a two-by-two system of boundary integral equations for the unknown boundary $$\\varGamma _0$$Γ0 and the unknown normal derivative $$g=\\partial _\\nu w$$g=źźw of w on $$\\varGamma _1$$Γ1. This system is nonlinear with respect to $$\\varGamma _0$$Γ0 and linear with respect to g and we suggest to solve it simultaneously for $$\\varGamma _0$$Γ0 and g by Newton iterations. We establish a local convergence result and exhibit the feasibility of the method by a few numerical examples. |
Year | DOI | Venue |
|---|---|---|
2017 | 10.1007/s00211-016-0847-5 | Numerische Mathematik |
Keywords | Field | DocType |
31A10, 35R35, 65R20, 76B07 | Boundary value problem,Mathematical optimization,Harmonic function,Mathematical analysis,Dirichlet boundary condition,Integral equation,Local convergence,Numerical analysis,Directional derivative,Mathematics,Bernoulli's principle | Journal |
Volume | Issue | ISSN |
136 | 2 | 0945-3245 |
Citations | PageRank | References |
1 | 0.43 | 1 |
Authors | ||
1 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| David Colton | 1 | 33 | 15.98 |