In this paper we present an a-posteriori error estimator for the mixed formulation of a linear parabolic problem, used for designing an efficient adaptive algorithm. Our space-time discretization consists of lowest order Raviart-Thomas finite element over graded meshes and discontinuous Galerkin method with variable time step. Finally, several examples show that the proposed method is efficient...

ABSTRACT: In this study, adaptive neuro-fuzzy inference system, and feed forward neural network as two artificial intelligence-based models along with conventional multiple linear regression model were used to predict the multi-station modelling of dissolve oxygen concentration at the downstream of Mathura City in India. The data used are dissolved oxygen, pH, biological oxygen demand and water...

For the optimal control problems governed by linear elliptic or parabolic state equations, a priori error estimates of the finite element approximation were established long ago, see [1, 2, 3, 4, 5]. In order to obtain a numerical solution of acceptable accuracy for the optimal control problem, the finite element meshes have to be refined according to a mesh refinement scheme. Adaptive finite e...

Finite element analyses of irregular structures require adaptive mesh refinement to achieve more accurate results in an efficient manner. This is also true for a non-conventional finite method with Kriging interpolation, called the Kriging-based (K-FEM). paper presents study automatic meshing procedures two-dimensional linear elasticity problems using K-FEM. The Matlab Partial Differential Equa...

In a 1988 article, Dziuk introduced a nodal finite element method for the Laplace-Beltrami equation on 2-surfaces approximated by a piecewise-linear triangulation, initiating a line of research into surface finite element methods (SFEM). Demlow and Dziuk built on the original results, introducing an adaptive method for problems on 2-surfaces, and Demlow later extended the a priori theory to 3-s...

Local adaptive grid refinement is an important technique in finite element methods. Its study can be traced back to the pioneering work [2] in one dimension. In recent years, mathematicians start to prove the convergence and optimal complexity of the adaptive procedure in multi-dimensions. [11] first proved an error reduction in the energy norm for the Poisson equation provided the initial mesh...

A multiphase-field model for the description of coalescence in a binary alloy is solved numerically using adaptive finite elements with high aspect ratio. The unknown of the multiphase-field model are the three phase fields (solid phase 1, solid phase 2, and liquid phase), a Lagrange multiplier and the concentration field. An Euler implicit scheme is used for time discretization, together with ...

We give some fundamental results on the error constants for the piecewise constant interpolation function and the piecewise linear one over triangles. For the piecewise linear one, we mainly analyze the conforming case, but some results are also given for the non-conforming case. We obtain explicit relations for the dependence of such error constants on the geometric parameters of triangles. In...

A computationally efficient global optimization method, the adaptive particle swarm optimization (APSO), is proposed for the synthesis of uniform and Gaussian amplitude arrays of two cases, i.e., the prior constraint in the synthesis of the element positions for both the cases is dmin = 0.5 λ, where dmin is the minimum distance between two adjacent elements. The upper limit in the distance betw...