Articles citing this article

The Citing articles tool gives a list of articles citing the current article.
The citing articles come from EDP Sciences database, as well as other publishers participating in CrossRef Cited-by Linking Program. You can set up your personal account to receive an email alert each time this article is cited by a new article (see the menu on the right-hand side of the abstract page).

Cited article:

A Shape-Newton Method for Free-Boundary Problems Subject to the Bernoulli Boundary Condition

Yiyun Fan, John Billingham and Kristoffer G. van der Zee
SIAM Journal on Scientific Computing 46 (6) A3599 (2024)
https://doi.org/10.1137/23M1590263

Numerical Solution to a Free Boundary Problem for the Stokes Equation Using the Coupled Complex Boundary Method in Shape Optimization Setting

Julius Fergy Tiongson Rabago and Hirofumi Notsu
Applied Mathematics & Optimization 89 (1) (2024)
https://doi.org/10.1007/s00245-023-10065-7

Numerical solution to the exterior Bernoulli problem using the Dirichlet-Robin energy gap cost functional approach in two and three dimensions

Julius Fergy T. Rabago
Numerical Algorithms 94 (1) 175 (2023)
https://doi.org/10.1007/s11075-023-01497-x

A physics-informed learning approach to Bernoulli-type free boundary problems

Salvatore Cuomo, Fabio Giampaolo, Stefano Izzo, et al.
Computers & Mathematics with Applications 128 34 (2022)
https://doi.org/10.1016/j.camwa.2022.10.003

On the new coupled complex boundary method in shape optimization framework for solving stationary free boundary problems

Julius Fergy T. Rabago
Mathematical Control and Related Fields (2022)
https://doi.org/10.3934/mcrf.2022041

Solving a Bernoulli type free boundary problem with random diffusion

Rahel Brügger, Roberto Croce and Helmut Harbrecht
ESAIM: Control, Optimisation and Calculus of Variations 26 56 (2020)
https://doi.org/10.1051/cocv/2019030

A second-order shape optimization algorithm for solving the exterior Bernoulli free boundary problem using a new boundary cost functional

Julius Fergy T. Rabago and Hideyuki Azegami
Computational Optimization and Applications 77 (1) 251 (2020)
https://doi.org/10.1007/s10589-020-00199-7

Shape optimization and subdivision surface based approach to solving 3D Bernoulli problems

Jan Zapletal and Jiří Bouchala
Computers & Mathematics with Applications 78 (9) 2911 (2019)
https://doi.org/10.1016/j.camwa.2019.02.015

An improved shape optimization formulation of the Bernoulli problem by tracking the Neumann data

Julius Fergy T. Rabago and Hideyuki Azegami
Journal of Engineering Mathematics 117 (1) 1 (2019)
https://doi.org/10.1007/s10665-019-10005-x

A cut finite element method for the Bernoulli free boundary value problem

Erik Burman, Daniel Elfverson, Peter Hansbo, Mats G. Larson and Karl Larsson
Computer Methods in Applied Mechanics and Engineering 317 598 (2017)
https://doi.org/10.1016/j.cma.2016.12.021

Numerical Mathematics and Advanced Applications - ENUMATH 2013

P. F. Antonietti, Nadia Bigoni and Marco Verani
Lecture Notes in Computational Science and Engineering, Numerical Mathematics and Advanced Applications - ENUMATH 2013 103 125 (2015)
https://doi.org/10.1007/978-3-319-10705-9_12

Trends in PDE Constrained Optimization

Helmut Harbrecht and Johannes Tausch
International Series of Numerical Mathematics, Trends in PDE Constrained Optimization 165 213 (2014)
https://doi.org/10.1007/978-3-319-05083-6_14

Mimetic finite differences for nonlinear and control problems

P. F. Antonietti, L. Beirão da Veiga, N. Bigoni and M. Verani
Mathematical Models and Methods in Applied Sciences 24 (08) 1457 (2014)
https://doi.org/10.1142/S0218202514400016

Improved trial methods for a class of generalized Bernoulli problems

Helmut Harbrecht and Giannoula Mitrou
Journal of Mathematical Analysis and Applications 420 (1) 177 (2014)
https://doi.org/10.1016/j.jmaa.2014.05.059

The Second-Order Shape Derivative of Kohn–Vogelius-Type Cost Functional Using the Boundary Differentiation Approach

Jerico Bacani and Gunther Peichl
Mathematics 2 (4) 196 (2014)
https://doi.org/10.3390/math2040196

On Computation of the Shape Hessian of the Cost Functional Without Shape Sensitivity of the State Variable

H. Kasumba and K. Kunisch
Journal of Optimization Theory and Applications 162 (3) 779 (2014)
https://doi.org/10.1007/s10957-013-0520-4

Numerical approximation of one phase quadrature domains

Mahmoudreza Bazarganzadeh and Farid Bozorgnia
Numerical Methods for Partial Differential Equations 29 (5) 1709 (2013)
https://doi.org/10.1002/num.21773

A Dirichlet–Neumann cost functional approach for the Bernoulli problem

A. Ben Abda, F. Bouchon, G. H. Peichl, M. Sayeh and R. Touzani
Journal of Engineering Mathematics 81 (1) 157 (2013)
https://doi.org/10.1007/s10665-012-9608-3

On the First-Order Shape Derivative of the Kohn-Vogelius Cost Functional of the Bernoulli Problem

Jerico B. Bacani and Gunther Peichl
Abstract and Applied Analysis 2013 1 (2013)
https://doi.org/10.1155/2013/384320

Constrained Optimization and Optimal Control for Partial Differential Equations

Karsten Eppler and Helmut Harbrecht
International Series of Numerical Mathematics, Constrained Optimization and Optimal Control for Partial Differential Equations 160 277 (2012)
https://doi.org/10.1007/978-3-0348-0133-1_15

Two Adjoint-Based Optimization Approaches for a Free Surface Stokes Flow

Sabine Repke, Nicole Marheineke and René Pinnau
SIAM Journal on Applied Mathematics 71 (6) 2168 (2011)
https://doi.org/10.1137/100797953

Tracking Neumann Data for Stationary Free Boundary Problems

Karsten Eppler and Helmut Harbrecht
SIAM Journal on Control and Optimization 48 (5) 2901 (2010)
https://doi.org/10.1137/080733760

An inverse model for a free-boundary problem with a contact line: Steady case

Oleg Volkov and Bartosz Protas
Journal of Computational Physics 228 (13) 4893 (2009)
https://doi.org/10.1016/j.jcp.2009.03.042

On Convergence in Elliptic Shape Optimization

Karsten Eppler, Helmut Harbrecht and Reinhold Schneider
SIAM Journal on Control and Optimization 46 (1) 61 (2007)
https://doi.org/10.1137/05062679X