Out of the wide range of a-posteriori error estimates for the Finite Element Method (FEM) of discretisation, the group of estimates based on the element residual seems to be the most popular. One recent extension of the Element Residual Method is the Local Problem Error Estimate (LPEE) 1], which includes the elements of the duality theory and consistently produces good results with the ef-fecti...

The investigation of fatigue strength needs an accurate solution and reliable values of the stress intensity factor (SIF). In this study, SIF of load-carrying cruciform welded joints has been evaluated using finite element method (FEM), and compared with the available solutions from literature. Load-carrying cruciform welded joints with isosceles triangles and non-isosceles triangle fillet weld...

We present three new a posteriori error estimators in the energy norm for finite element solutions to elliptic partial differential equations. The estimators are based on solving local Neumann problems in each element. The estimators differ in how they enforce consistency of the Neumann problems. We prove that as the mesh size decreases, under suitable assumptions, two of the error estimators a...

To validate the reasonableness of a numerical solution to a partial differential equation on a given mesh, a common approach is to refine the mesh, compute a solution on the finer mesh, and compare the solutions on the two meshes. Comparing graphical representations of the two solutions gives a qualitative assessment of the solution quality. In many cases though, a priori error estimates from t...

Abatmet-Some basic studies and developments for adaptive procedures in large strain finite element analysis are presented an evaluation of higher-order elements, two pointwise indiitors for errors in stresses, a mesh generator for remeshing on the deformed contiffuration of the body, and a general mapping scheme for transferring solution variables across models. The methods discus4 constitute t...

In this paper, free and forced vibration analysis of functionally graded material cylinders was carried out by mesh-free and finite element method. In this analysis, MLS shape functions are used for approximation of displacement field in the weak form of motion equation and essential boundary conditions are imposed by transformation method. Resulted set of differential equations are solved usin...

Researchers have developedmanymodels to simulate the elasto-plastic contact of spheres. However, there does not appear to exist a closed-form analytical model for elasto-plastic three-dimensional sinusoidal contact. This work uses a finite element model (FEM) to characterize elasto-plastic sinusoidal contact. Although at initial contact the sphere and sinusoidal case are very similar and can bo...

In this paper, we investigate the L∞-error estimates for the solutions of general optimal control problem by mixed finite element methods. The state and co-state are approximated by the lowest order Raviart-Thomas mixed finite element spaces and the control is approximated by piecewise constant functions. We derive L∞-error estimates of optimal order both for the state variables and the control...

A method for adaptive construction of nearly optimal nite element meshes is presented. The method is based on the notion of mesh density. For parametrized problems optimal meshes for new parameter values can be predicted from previous meshes. The method is of the one shot type, normally giving a suuciently good approiximation to the optimal mesh in the rst attempt , but when the rst shot is uns...

Article history: Received 10 October 2017 Accepted 7 January 2018