Related papers: Shape minimization problems in liquid crystals
We provide a framework for the numerical approximation of distributed optimal control problems, based on least-squares finite element methods. Our proposed method simultaneously solves the state and adjoint equations and is $\inf$--$\sup$…
We study a finite element approximation of a coupled fluid-structure interaction consisting of a three-dimensional incompressible viscous fluid governed by the unsteady Stokes equations and a two-dimensional elastic plate. To avoid the use…
Levitated nanospheres in optical cavities open a novel route to study many-body systems out of solution and highly isolated from the environment. We show that properly tuned optical parameters allow for the study of the non-equilibrium…
In general, standard necessary optimality conditions cannot be formulated in a straightforward manner for semi-smooth shape optimization problems. In this paper, we consider shape optimization problems constrained by variational…
Despite its numerical challenges, finite element method is used to compute viscous fluid flow. A consensus on the cause of numerical problems has been reached; however, general algorithms---allowing a robust and accurate simulation for any…
A finite element method for elliptic problems with discontinuous coefficients is presented. The discontinuity is assumed to take place along a closed smooth curve. The proposed method allows to deal with meshes that are not adapted to the…
Phase transition problems on curved surfaces can lead to a panopticon of fascinating patterns. In this paper we consider finite element approximations of phase field models with a spatially inhomogeneous and anisotropic surface energy…
We propose and analyze an unfitted finite element method for solving elliptic problems on domains with curved boundaries and interfaces. The approximation space on the whole domain is obtained by the direct extension of the finite element…
A new field of numerical astrophysics is introduced which addresses the solution of large, multidimensional structural or slowly-evolving problems (rotating stars, interacting binaries, thick advective accretion disks, four dimensional…
This paper aims to study the convergence of adaptive finite element method for control constrained elliptic optimal control problems under $L^2$-norm. We prove the contraction property and quasi-optimal complexity for the $L^2$-norm errors…
According to the Wulff construction the shape of the equilibrium crystal is determined by the surface tension considered as a function of the interface orientation. We present some (conjectured) approximate solutions and some rigorous…
We present and analyze a new finite element method for solving interface problems on a triangular grid. The method locally modifies a given triangulation such that the interfaces are accurately resolved and the maximal angle condition…
We consider the approximation of the 2D frictionless contact problem in elasticity using the Virtual Element Methods (VEMs). To overcome the volumetric locking phenomenon in the nearly incompressible case, we adopt a mixed…
This work presents a novel numerical investigation of the dynamics of free-boundary flows of viscoelastic liquid membranes. The governing equation describes the balance of linear momentum, in which the stresses include the viscoelastic…
In this paper, we consider a class of time-optimal control problems governed by linear parabolic equations with mixed control-state constraints and end-point constraints, and without Tikhonov regularization term in the objective function.…
Selective laser melting is receiving increasing interest as an additive manufacturing technique. Residual stresses induced by the large temperature gradients and inhomogeneous cooling process can favour the generation of cracks. In this…
We consider planar liquid crystal elastomers: two dimensional objects made of anisotropic responsive materials, that upon activation remain flat however change their planar shape. We derive a closed form, analytical solution based on the…
Achieving quantum-limited motional control of optically trapped particles beyond the sub-micrometer scale is an outstanding problem in levitated optomechanics. A key obstacle is solving the light scattering problem and identifying particle…
Manipulating the shape of a liquid droplet is essential for a wide range of applications in medicine and industry. However, existing methods are typically limited to generating simple shapes, such as ellipses, or rely on predefined…
A level set topology optimization approach that uses an auxiliary density field to nucleate holes during the optimization process and achieves minimum feature size control in optimized designs is explored. The level set field determines the…