... material laws. Design/methodology/approach To obtain new methods of error representation for a posteriori and goal-oriented error estimators, weak forms of primal and dual problems are investigated starting with the initial boundary value problem (IBVP). Then, we approximate both problems...

... refinement algorithm for eigenproblems in system of second-order ODEs, that can be extended to other classes of applications in damage detection of multiple cracks in structures based on the high-precision eigensolutions. Free vibration Error estimation Coincident eigenvalues h-version mesh...

... differential equations Modified Adomian decomposition method Adomian polynomials Convergence analysis Error estimation Singular initial value problems play an important role in the field of scientific disciplines. In this article, we consider a singular initial value problem of Lane–Emden type...

... is used to model elasto-plasticity and total Lagrangian formulations are used to model finite deformation. Furthermore, Zienkiewicz and Zhu and Chung and Belytschko error estimation procedure are used in the FE and meshless regions of the problem domain, respectively. The message passing interface library...

... the singular solution; also the accuracy, local and global effectivity of recovery‐based error estimators for enriched finite element methods (e.g. the extended finite element method, XFEM). Design/methodology/approach The authors study the performance of two recovery techniques. The first is a recently...

... error estimator and a h‐refinement procedure are used to obtain the non‐nested meshes used by the multigrid methods. We solve problems with a specified percentage error in the energy norm using the optimal performance of multigrid methods. © MCB UP Limited 2002 Error estimation...

.... For 3‐D acoustic vibration problem, the element energies are (6) © MCB UP Limited 1998 Eigenproblems Error estimation Finite element Patch recovery In static FE problems, discretization error derives from the stiffness matrix, while in vibration problems it derives from both...

... to be adapted such that the crack path remains independent of the initial mesh. The accuracy of the obtained results has to be controlled by suitable error estimators and error indicators. Considering the dependence of the predicted crack path on the precision of the displacement and stress computation, quality...

... or p. Adaptive meshing refinement Error estimation Strain energy density Up to a few years ago the reliability of the finite element method (FEM) depended heavily on the experience and ability of the user, but the tendency in the meantime has been to eliminate those tasks that involved...

... of the exact eigenvalue λ is unknown, so it may be replaced with the improved eigenvalue λ^* to give an error estimate ε^*, based on this value to represent the actual error. This error estimate is expressed as: (5) All papers[ 2 , 3 , 4 , 5 , 6...

... with the minimum computational resources in terms of computing time and storage. To this extent, convergence studies are performed with constant and variable adaptivity indices, with error estimators based on global and elemental approaches and with domain decomposition matrix‐handling techniques...

...A. Dutta; C.V. Ramakrishnan Presents a method of obtaining an optimal mesh in the finite element analysis of two‐dimensional linear elastodynamic problems under transient dynamic loading, which is based on a generalization of the Z‐Z criterion for discretization error estimation for time...

... ESTEREF , a post‐processor of error computation and mesh optimization that can be used with any finite element code. Numerous examples show the capabilities of the proposed method. © MCB UP Limited 1994 Steep gradients Finite elements Error estimation Mesh optimization ENGINEERING...

... optimization which can be interfaced with any finite element code. © MCB UP Limited 1991 Elasticity problems Finite elements Error estimation Mesh optimization ENGINEERING COMPUTATIONS, VOL. 8, 69-80 (1991) ERROR ESTIMATION AND MESH OPTIMIZATION FOR CLASSICAL FINITE ELEMENTS P. LADEVÈZE, J.-P...

...A. Selman; E. Hinton; W. Atamaz‐Sibai An adaptive mesh refinement procedure is used in static plate bending finite element analysis to study the edge effects in Mindlin—Reissner plates. © MCB UP Limited 1990 Mindlin—Reissner plate theory boundary layer error estimation adaptivity...