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Posteriori Error Analysis (posteriori + error_analysis)
Selected AbstractsOn the a priori and a posteriori error analysis of a two-fold saddle-point approach for nonlinear incompressible elasticityINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 8 2006Gabriel N. Gatica Abstract In this paper, we reconsider the a priori and a posteriori error analysis of a new mixed finite element method for nonlinear incompressible elasticity with mixed boundary conditions. The approach, being based only on the fact that the resulting variational formulation becomes a two-fold saddle-point operator equation, simplifies the analysis and improves the results provided recently in a previous work. Thus, a well-known generalization of the classical Babu,ka,Brezzi theory is applied to show the well-posedness of the continuous and discrete formulations, and to derive the corresponding a priori error estimate. In particular, enriched PEERS subspaces are required for the solvability and stability of the associated Galerkin scheme. In addition, we use the Ritz projection operator to obtain a new reliable and quasi-efficient a posteriori error estimate. Finally, several numerical results illustrating the good performance of the associated adaptive algorithm are presented. Copyright © 2006 John Wiley & Sons, Ltd. [source] c-Type method of unified CAMG and FEA.INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 9 20032D non-linear, 3D linear, Part 1: Beam, arch mega-elements Abstract Computer-aided mesh generation (CAMG) dictated solely by the minimal key set of requirements of geometry, material, loading and support condition can produce ,mega-sized', arbitrary-shaped distorted elements. However, this may result in substantial cost saving and reduced bookkeeping for the subsequent finite element analysis (FEA) and reduced engineering manpower requirement for final quality assurance. A method, denoted as c-type, has been proposed by constructively defining a finite element space whereby the above hurdles may be overcome with a minimal number of hyper-sized elements. Bezier (and de Boor) control vectors are used as the generalized displacements and the Bernstein polynomials (and B-splines) as the elemental basis functions. A concomitant idea of coerced parametry and inter-element continuity on demand unifies modelling and finite element method. The c-type method may introduce additional control, namely, an inter-element continuity condition to the existing h-type and p-type methods. Adaptation of the c-type method to existing commercial and general-purpose computer programs based on a conventional displacement-based finite element method is straightforward. The c-type method with associated subdivision technique can be easily made into a hierarchic adaptive computer method with a suitable a posteriori error analysis. In this context, a summary of a geometrically exact non-linear formulation for the two-dimensional curved beams/arches is presented. Several beam problems ranging from truly three-dimensional tortuous linear curved beams to geometrically extremely non-linear two-dimensional arches are solved to establish numerical efficiency of the method. Incremental Lagrangian curvilinear formulation may be extended to overcome rotational singularity in 3D geometric non-linearity and to treat general material non-linearity. Copyright © 2003 John Wiley & Sons, Ltd. [source] Anisotropic mesh adaption for time-dependent problems,INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 9 2008S. Micheletti Abstract We propose a space,time adaptive procedure for a model parabolic problem based on a theoretically sound anisotropic a posteriori error analysis. A space,time finite element scheme (continuous in space but discontinuous in time) is employed to discretize this problem, thus allowing for non-matching meshes at different time levels. Copyright © 2008 John Wiley & Sons, Ltd. [source] | ||||||||||