相关论文: Optimal Control of the Laplace-Beltrami operator o…

We consider a linear-quadratic optimization problem with pointwise bounds on the state for which the constraint is given by the Laplace-Beltrami equation (to have uniqueness we add an lower order term) on a two-dimensional surface . By…

We consider an elliptic optimal control problem where the objective functional contains an integral along a surface of codimension 1, also known as a hypersurface. In particular, we use a fidelity term that encourages the state to take…

We adopt the integral definition of the fractional Laplace operator and analyze solution techniques for fractional, semilinear, and elliptic optimal control problems posed on Lipschitz polytopes. We consider two strategies of…

We adopt the integral definition of the fractional Laplace operator and analyze an optimal control problem for a fractional semilinear elliptic partial differential equation (PDE); control constraints are also considered. We establish the…

The convergence problem of the Laplace-Beltrami operators plays an essential role in the convergence analysis of the numerical simulations of some important geometric partial differential equations which involve the operator. In this note…

We develop a finite element method for the Laplace--Beltrami operator on a surface described by a set of patchwise parametrizations. The patches provide a partition of the surface and each patch is the image by a diffeomorphism of a…

We consider an elliptic optimal control problem where the objective functional contains evaluations of the state at a finite number of points. In particular, we use a fidelity term that encourages the state to take certain values at these…

The Laplace-Beltrami operator on (the surface of) a triaxial ellipsoid admits a sequence of real eigenvalues diverging to plus infinity. By introducing ellipsoidal coordinates, this eigenvalue problem for a partial differential operator is…

We adopt the integral definition of the fractional Laplace operator and study an optimal control problem on Lipschitz domains that involves a fractional elliptic partial differential equation (PDE) as state equation and a control variable…

We propose in this paper a multilevel correction method to solve optimal control problems constrained by elliptic equations with the finite element method. In this scheme, solving optimization problem on the finest finite element space is…

We consider an abstract framework for the numerical solution of optimal control problems (OCPs) subject to partial differential equations (PDEs). Examples include not only the distributed control of elliptic PDEs such as the Poisson…

Computational approaches to PDE-constrained optimization under uncertainty may involve finite-dimensional approximations of control and state spaces, sample average approximations of measures of risk and reliability, smooth approximations…

This paper studies an optimal control problem governed by a semilinear elliptic equation, in which the control acts in a multiplicative or bilinear way as the reaction coefficient of the equation. We focus on the numerical discretization of…

We present a new parallel computational framework for the efficient solution of a class of $L^2$/$L^1$-regularized optimal control problems governed by semi-linear elliptic partial differential equations (PDEs). The main difficulty in…

We discuss several optimization procedures to solve finite element approximations of linear-quadratic Dirichlet optimal control problems governed by an elliptic partial differential equation posed on a 2D or 3D Lipschitz domain. The control…

In this work is considered a spectral problem, involving a second order term on the domain boundary: the Laplace-Beltrami operator. A variational formulation is presented, leading to a finite element discretization. For the Laplace-Beltrami…

We suggest a finite element method for computing minimal surfaces based on computing a discrete Laplace-Beltrami operator operating on the coordinates of the surface. The surface is a discrete representation of the zero level set of a…

We study an optimal control problem governed by elliptic PDEs with interface, which the control acts on the interface. Due to the jump of the coefficient across the interface and the control acting on the interface, the regularity of…

This work investigates an elliptic optimal control problem defined on uncertain domains and discretized by a fictitious domain finite element method and cut elements. Key ingredients of the study are to manage cases considering the usually…

We develop a finite element method for the Laplace-Beltrami operator on a surface with boundary and nonhomogeneous Dirichlet boundary conditions. The method is based on a triangulation of the surface and the boundary conditions are enforced…