A Numerical Method for Steady State Free Boundary Problems
SIAM Journal on Numerical Analysis
Shapes and geometries: analysis, differential calculus, and optimization
Shapes and geometries: analysis, differential calculus, and optimization
hp-Adaptive Discontinuous Galerkin Finite Element Methods for First-Order Hyperbolic Problems
SIAM Journal on Scientific Computing
Convergence of Adaptive Finite Element Methods
SIAM Review
Adaptive Discontinuous Galerkin Finite Element Methods for Nonlinear Hyperbolic Conservation Laws
SIAM Journal on Scientific Computing
Computational Optimization and Applications
Adaptive Finite Element Methods with convergence rates
Numerische Mathematik
SIAM Journal on Scientific Computing
Efficient treatment of stationary free boundary problems
Applied Numerical Mathematics - Selected papers from the first Chilean workshop on numerical analysis of partial differential equations (WONAPDE 2004)
Optimality of a Standard Adaptive Finite Element Method
Foundations of Computational Mathematics
On Convergence in Elliptic Shape Optimization
SIAM Journal on Control and Optimization
Fast Numerical Methods for Bernoulli Free Boundary Problems
SIAM Journal on Scientific Computing
Multitarget Error Estimation and Adaptivity in Aerodynamic Flow Simulations
SIAM Journal on Scientific Computing
A Goal-Oriented Adaptive Finite Element Method with Convergence Rates
SIAM Journal on Numerical Analysis
A Newton method using exact jacobians for solving fluid-structure coupling
Computers and Structures
SIAM Journal on Scientific Computing
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In free-boundary problems, the accuracy of a goal quantity of interest depends on both the accuracy of the approximate solution and the accuracy of the domain approximation. We develop duality-based a posteriori error estimates for functional outputs of solutions of free-boundary problems that include both sources of error. The derivation of an appropriate dual problem (linearized adjoint) is, however, nonobvious for free-boundary problems. To derive an appropriate dual problem, we present the domain-map linearization approach. In this approach, the free-boundary problem is first transformed into an equivalent problem on a fixed reference domain after which the dual problem is obtained by linearization with respect to the domain map. We show for a Bernoulli-type free-boundary problem that this dual problem corresponds to a Poisson problem with a nonlocal Robin-type boundary condition. Furthermore, we present numerical experiments that demonstrate the effectivity of the dual-based error estimate and its usefulness in goal-oriented adaptive mesh refinement.