Related papers: Numerical solution to a free boundary problem for …
Many physical systems of interest involve the close interaction of a flow in a domain with complex, time-varying boundaries. Treatment of boundaries of this nature is cumbersome due to the difficulty in explicitly tracking boundaries that…
The immersed boundary method is a mathematical formulation and numerical method for solving fluid-structure interaction problems. For many biological problems, such as models that include the cell membrane, the immersed structure is a…
The aim of this work is to point out that the class of free boundary problems governed by second order autonomous ordinary differential equations can be transformed to initial value problems. Interest in the numerical solution of free…
In [ESAIM: M2AN, 54(2020), 2229-2264], we proposed an HDG method to approximate the solution of a tangential boundary control problem for the Stokes equations and obtained an optimal convergence rate for the optimal control {that reflects…
Numerical algorithms for solving problems of mathematical physics on modern parallel computers employ various domain decomposition techniques. Domain decomposition schemes are developed here to solve numerically initial/boundary value…
We consider the generalized Stokes resolvent problem in an infinite layer with Neumann boundary conditions. This problem arises from a free boundary problem describing the motion of incompressible viscous one-phase fluid flow without…
Variational approaches have been used successfully as a strategy to take advantage from real data measurements. In several applications, this approach gives a means to increase the accuracy of numerical simulations. In the particular case…
The Stokes equations play an important role in the incompressible flow simulation. In this paper, a novel divergence-free parametric mixed finite element method is proposed for solving three-dimensional Stokes equations on domains with…
We review the first and second boundary value problems for the Stokes system posed in a bounded Lipschitz domain in $\mathbb{R}^n.$ Particular attention is given to the mixed boundary condition: a Dirichlet condition is imposed for the…
The purpose of this paper is to analyze and compute the early exercise boundary for a class of nonlinear Black--Scholes equations with a nonlinear volatility which can be a function of the second derivative of the option price itself. A…
A new approach to the solution of boundary value problems within the so-called fictitious domain methods philosophy is proposed which avoids well known shortcomings of other fictitious domain methods, including the need to generate…
The presence of surfactants alters the dynamics of viscous drops immersed in an ambient viscous fluid. This is specifically true at small scales, such as in applications of droplet based microfluidics, where the interface dynamics become of…
Some approach to the solution of boundary value problems for finding functions, which are analytical in a wedge, is proposed. If the ratio of the angle at the wedge vertex to a number \pi is rational, then the boundary value problem is…
In this paper we apply the recently developed mimetic discretization method to the mixed formulation of the Stokes problem in terms of vorticity, velocity and pressure. The mimetic discretization presented in this paper and in [50] is a…
For shape optimization problems, governed by elliptic equations with Dirichlet boundary condition and random coefficients, we utilize a penalization technique to get the approximate problem. We consider that uncertainties exists in the…
Periodic travelling waves at the free surface of an incompressible inviscid fluid in two dimensions under gravity are numerically computed for an arbitrary vorticity distribution. The fluid domain over one period is conformally mapped from…
This paper presents computational analysis of the inverse Stefan type free boundary problem, where information on the boundary heat flux is missing and must be found along with the temperature and the free boundary. We pursue optimal…
In this article we consider shape optimization problems as optimal control problems via the method of mappings. Instead of optimizing over a set of admissible shapes a reference domain is introduced and it is optimized over a set of…
Conventional mathematical models for simulating incompressible fluid flow problems are based on the Navier-Stokes equations expressed in terms of pressure and velocity. In this context, pressure-velocity coupling is a key issue, and…
We propose an efficient threshold dynamics method for topology optimization for fluids modeled with the Stokes equation. The proposed algorithm is based on minimization of an objective energy function that consists of the dissipation power…