Premium
Stabilization of the trial method for the Bernoulli problem in case of prescribed Dirichlet data
Author(s) -
Harbrecht Helmut,
Mitrou Giannoula
Publication year - 2014
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3268
Subject(s) - mathematics , mixed boundary condition , neumann boundary condition , boundary value problem , robin boundary condition , mathematical analysis , dirichlet boundary condition , free boundary problem , bernoulli's principle , cauchy boundary condition , poincaré–steklov operator , elliptic boundary value problem , boundary (topology) , linearization , singular boundary method , boundary element method , finite element method , nonlinear system , physics , quantum mechanics , engineering , thermodynamics , aerospace engineering
We apply the trial method for the solution of Bernoulli's free boundary problem when the Dirichlet boundary condition is imposed for the solution of the underlying Laplace equation, and the free boundary is updated according to the Neumann boundary condition. The Dirichlet boundary value problem for the Laplacian is solved by an exponentially convergent boundary element method. The update rule for the free boundary is derived from the linearization of the Neumann data around the actual free boundary. With the help of shape sensitivity analysis and Banach's fixed‐point theorem, we shed light on the convergence of the respective trial method. Especially, we derive a stabilized version of this trial method. Numerical examples validate the theoretical findings.Copyright © 2014 John Wiley & Sons, Ltd.
Accelerating Research
Robert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom
Address
John Eccles HouseRobert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom