Related papers: On the convergence of fixed point iterations for t…
In a recent paper~\cite{paper2}, we proposed the concept of optimal error bounds for an iterative process, which allows us to obtain the convergence result of the iterative sequence to the common fixed point of the nonexpansive mappings in…
We propose a fluid-rigid body interaction benchmark problem, consisting of a solid spherical obstacle in a Newtonian fluid, whose centre of mass is fixed but is free to rotate. A number of different problems are defined for both two and…
Both Newtonian and non-Newtonian fluids may exhibit complex slip behaviour at the boundary. We examine a broad class of slip boundary conditions that generalises the commonly used Navier slip, perfect slip, stick-slip and Tresca friction…
The geometric motion of small droplets placed on an impermeable textured substrate is mainly driven by the capillary effect, the competition among surface tensions of three phases at the moving contact lines, and the impermeable substrate…
We study a thermodynamically consistent diffuse-interface model that describes the motion of two macroscopically immiscible, incompressible, and viscous Newtonian fluids with unmatched densities. This model is compatible with continuum…
We present a novel framework inspired by the Immersed Boundary Method for predicting the fluid-structure interaction of complex structures immersed in flows with moderate to high Reynolds numbers. The main novelties of the proposed…
We point out how Banach Fixed Point Theorem, and the Picard successive approximation methods induced by it, allows us to treat some mathematical methods in Combinatorics. In particular we get, by this way, a proof and an iterative algorithm…
This paper presents a general and robust method for the fluid-structure interaction of membranes and shells undergoing large displacement and large added-mass effects by coupling an immersed-boundary method with a shell finite-element…
In this paper, we study a new iterative method for a common fixed point of a finite family of Bregman strongly nonexpansive mappings in the frame work of reflexive real Banach spaces. Moreover, we prove the strong convergence theorem for…
In this paper, we propose a globally convergent method for solving constrained nonlinear systems. The method combines an efficient Newton conditional gradient method with a derivative-free and nonmonotone linesearch strategy. The global…
This paper deals with a modified iterative projection method for approximating a solution of the hierarchical fixed point problem for a sequene of nearly nonexpansive mappings with respect to a nonexpansive mapping. It is shown that under…
We studied numerically the dynamics of colliding rigid bodies in a Newtonian fluid. The finite element method is used to solve the fluid-body interaction and the fluid motion is described in the Arbitrary-Lagrangian-Eulerian framework. To…
We developed a computational framework for simulating thin fluid flow in narrow interfaces between contacting solids, which is relevant for a range of engineering, biological and geophysical applications. The treatment of this problem…
Let $X$ be a real Banach space with a normalized duality mapping uniformly norm-to-weak$^\star$ continuous on bounded sets or a reflexive Banach space which admits a weakly continuous duality mapping $J_{\Phi}$ with gauge $\phi$. Let $f$ be…
We study a fluid-structure interaction problem describing movement of a rigid body inside a bounded domain filled by a viscous fluid. The fluid is modelled by the generalized incompressible Naiver-Stokes equations which include cases of…
In this work we numerically explore the Newton-Raphson basins of convergence, related to the equilibrium points, in the Sitnikov three-body problem with non-spherical primaries. The evolution of the position of the roots is determined, as a…
We consider a fluid-structure interaction model for an incompressible fluid where the elastic response of the free boundary is given by a damped Kirchhoff plate model. Utilizing the Newton polygon approach, we first prove maximal regularity…
In this paper, a general hybrid fixed point theorem for the contractive mappings in generalized Banach spaces is proved via measure of weak non-compactness and it is further applied to fractional integral equations for proving the existence…
This work addresses research questions arising from the application of geometrically exact beam theory in the context of fluid-structure interaction (FSI). Geometrically exact beam theory has proven to be a computationally efficient way to…
An algorithm is proposed for generalized mean curvature flow of closed two-dimensional surfaces, which include inverse mean curvature flow, powers of mean and inverse mean curvature flow, etc. Error estimates are proven for semi- and full…