Several results on existence and convergence of the Yang-Mills flow in dimension four are given. We show that a singularity modeled on an instanton cannot form within finite time. Given low initial self-dual energy, we then study convergence of the flow at infinite time. If an Uhlenbeck limit is anti-self-dual and has vanishing self-dual second cohomology, then no bubbling occurs and the flow c...

We show that a piecewise linear finite element approximation of the obstacle problem gives an approximate free boundary converges, in an appropriate distance, to the free boundary of the continuous problemunder a stability condition on the obstacle.

We show that gradient descent converges to a local minimizer, almost surely with random initialization. This is proved by applying the Stable Manifold Theorem from dynamical systems theory.

We study the links between the values of stochastic games with varying stage duration h, the corresponding Shapley operators T and Th = hT+ (1− h)Id and the solution of the evolution equation ḟt = (T − Id)ft. Considering general non expansive maps we establish two kinds of results, under both the discounted or the finite length framework, that apply to the class of “exact” stochastic games. Fir...

We propose a mixed finite element method for the motion of a strongly viscous, ideal, and isentropic gas. At the boundary we impose a Navier–slip condition such that the velocity equation can be posed in mixed form with the vorticity as an auxiliary variable. In this formulation we design a finite element method, where the velocity and vorticity is approximated with the divand curlconforming Né...

This paper presents a sliding mode filter for removing noise. It effectively removes impulsive noise and high-frequency noise with producing smaller phase lag than linear filters. In addition, it is less prone to overshoot than previous sliding mode filters and it does not produce chattering. It is computationally inexpensive, and thus suitable for realtime applications. The proposed sliding mo...

In this article we propose an efficient numerical scheme based on a Shishkin mesh for a class of singularly perturbed parabolic convection-diffusion problems with boundary turning point and retarded arguments. The solution of the considered problem exhibit a boundary layer on the left side of the domain. The continuous problem is semidiscretized by means of backward Euler finite difference meth...

In this paper, a numerical method for solving the constrained optimal control of time-varying singular systems with quadratic performance index is presented. Presented method is based on Bernste in polynomials. Operational matrices of integration, differentiation and product are introduced and utilized to reduce the optimal control of time-varying singular problems to the solution of algebraic ...

Abstract Convergence of a finite element method with mass-lumping and flux upwinding is formulated for solving the immiscible two-phase flow problem in porous media. The approximates directly wetting phase pressure saturation, which are primary unknowns. Well-posedness obtained [J. Numer. Math., 29(2), 2021]. Theoretical convergence proved via compactness argument. numerical saturation converge...