In this paper, we propose an adaptive finite element algorithm for the numerical solution of a class of nonlocal models which correspond to nonlocal diffusion equations and linear scalar peridynamic models with certain non-integrable kernel functions. The convergence of the adaptive finite element algorithm is rigorously derived with the help of several basic ingredients, such as the upper boun...

We consider adaptive multilevel techniques for nonconforming nite element dis-cretizations of second order elliptic boundary value problems. In particular, we will focus on two basic ingredients of an eecient adaptive algorithm. The rst one is the iterative solution of the arising linear system by preconditioned conjugate gradient methods and the second one is an a posteriori error estimator fo...

let $g$ be a finite group. we construct the prime graph of $ g $,which is denoted by $ gamma(g) $ as follows: the vertex set of thisgraph is the prime divisors of $ |g| $ and two distinct vertices $ p$ and $ q $ are joined by an edge if and only if $ g $ contains anelement of order $ pq $.in this paper, we determine finite groups $ g $ with $ gamma(g) =gamma(l_3(q)) $, $2 leq q < 100 $ and prov...

The authors study here the problem of adaptive ”soft-landing” control for electromagnetic actuators. The soft landing requires accurate control of the actuator’s moving element between two desired positions. They propose a non-linear adaptive controller to solve the problem of robust trajectory tracking for the moving element, when considering model uncertainties with linear parametrisation. Th...

Natural indexing is an application-oriented description method for nite element meshes. This work describes how the main parts of an adaptive multilevel method for linear triangular nite element methods can be expressed within the framework of natural indexing. Particular emphasis is on the expression of operations that involve hierarchies of meshes such as adaptive re nement, hierarchic coarse...

An efficient adaptation technique of the delay is introduced for accomplishing more accurate adaptive linear equalization of nonminimum phase channels. It is focused that the filter structure and adaptation procedure of the adaptive Butler-Cantoni (ABC) equalizer is very suitable to deal with a variable delay for each iteration, compared with a classical adaptive linear transversal equalizer (L...

This paper studies a new recovery-based a posteriori error estimator for the conforming linear finite element approximation to elliptic interface problems. Instead of recovering the gradient in the continuous finite element space, the flux is recovered through a weighted L2 projection onto H(div) conforming finite element spaces. The resulting error estimator is analyzed by establishing the rel...

This paper investigates the adaptive solution of linear elastic structural analysis problems through re-positioning of the nite element nodal points (r-renement) using an approach known as the Moving Finite Element method. After a brief introduction to the Moving Finite Element method it is proved that this technique can yield optimal nite element solutions on optimal meshes in the energy norm ...