Abstract
The present article is concerned with solving Bernoulli’s exterior free boundary problem in the case of an interior boundary that is random. We provide a new regularity result on the map that sends a parametrization of the inner boundary to a parametrization of the outer boundary. Moreover, assuming that the interior boundary is convex, also the exterior boundary is convex, which enables to identify the boundaries with support functions and to determine their expectations. We in particular construct a confidence region for the outer boundary based on Aumann’s expectation and provide a numerical method to compute it.
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© 2022 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Recent Advances in Boundary Element Methods
- Fast Barrier Option Pricing by the COS BEM Method in Heston Model (with Matlab Code)
- Bernoulli Free Boundary Problems Under Uncertainty: The Convex Case
- CVEM-BEM Coupling for the Simulation of Time-Domain Wave Fields Scattered by Obstacles with Complex Geometries
- Developments on the Stability of the Non-symmetric Coupling of Finite and Boundary Elements
- Coupling of Finite and Boundary Elements for Singularly Nonlinear Transmission and Contact Problems
- BEM-Based Magnetic Field Reconstruction by Ensemble Kálmán Filtering
- Force Computation for Dielectrics Using Shape Calculus
- A Time-Adaptive Space-Time FMM for the Heat Equation
- Integral Representations and Quadrature Schemes for the Modified Hilbert Transformation
- High-Order Compact Finite Difference Methods for Solving the High-Dimensional Helmholtz Equations
- A Posteriori Error Estimates for Darcy–Forchheimer’s Problem
- Convergence of a Finite Difference Scheme for a Flame/Smoldering-Front Evolution Equation and Its Application to Wavenumber Selection
Artikel in diesem Heft
- Frontmatter
- Recent Advances in Boundary Element Methods
- Fast Barrier Option Pricing by the COS BEM Method in Heston Model (with Matlab Code)
- Bernoulli Free Boundary Problems Under Uncertainty: The Convex Case
- CVEM-BEM Coupling for the Simulation of Time-Domain Wave Fields Scattered by Obstacles with Complex Geometries
- Developments on the Stability of the Non-symmetric Coupling of Finite and Boundary Elements
- Coupling of Finite and Boundary Elements for Singularly Nonlinear Transmission and Contact Problems
- BEM-Based Magnetic Field Reconstruction by Ensemble Kálmán Filtering
- Force Computation for Dielectrics Using Shape Calculus
- A Time-Adaptive Space-Time FMM for the Heat Equation
- Integral Representations and Quadrature Schemes for the Modified Hilbert Transformation
- High-Order Compact Finite Difference Methods for Solving the High-Dimensional Helmholtz Equations
- A Posteriori Error Estimates for Darcy–Forchheimer’s Problem
- Convergence of a Finite Difference Scheme for a Flame/Smoldering-Front Evolution Equation and Its Application to Wavenumber Selection