Orthogonality constrained gradient reconstruction for. Locally equilibrated superconvergent patch recovery for. Recovery techniques were extended to enriched approximations in,14,15,16 and to hellingerreissner smoothingbased nite elements in. A modified superconvergent patch recovery method and its. Abstract in this paper, a 3d superconvergent patch recovery spr method is developed for data transferring in elastoplasticity. Using the linear virtual element method as an example, we propose a universal gradient recovery procedure to improve the accuracy of gradient approximation for numerical methods using general polygonal. The superconvergent patch recovery and a posteriori error.
Superconvergent patch recovery and a posteriori error. Famous examples include the simpleweighted averaging 55, superconvergent patch recovery 56,57 spr, and the polynomial preserving recovery 39,40,54 ppr. Recovery by equilibrium in patches rep is a recovery method introduced by b. Superconvergent patch recovery spr it is well known that for most elements, certain sampling points exist at which the values of o, have a greater accuracy and a higher order of convergence than elsewhere 710. These modifications are 1 use of integration points as sampling points, 2 weighted average procedure and 3 introduction of additional nodes. The recovery procedure consists of obtaining the improved nodal stresses, and then interpolating these values to other points using the element shape functions. Efficient finite element methodology based on cartesian.
Superconvergent patch recovery spr the original idea of spr was to improve the gradient value of the computed fe solution at nodal points. Patch recovery based on superconvergent derivatives and. Since the superconvergent patch scp recovery method is relativity easy to understand and is accurate for a wide range of problems, it was selected for implementation in the educational programmodel. Introduction in a coupled simulation of fluidstructure interaction fsi phenomena, the interesting unknowns for design decisions are the sectional forces caused by the dynamic fluid pressure acting on the surface of the structure. The potential advantage of these techniques is that generation of unit cell models can be automated, thus requiring far less human time than traditional finite element models. The superconvergent recovery technique developed in the first part of the paper 1 is the used in the computation of the zienkiewiczzhu error estimator to demonstrate accurate estimation of the exact error attainable. The zienkiewiczzhu error estimate is slightly modified for the hierarchical prefinement, and is then applied to three plane elastostatic problems to demonstrate. Superconvergent gradient recovery for virtual element methods. Mesh adaptivity driven by goaloriented locally equilibrated superconvergent patch recovery authors. Patchbased stress recovery techniques, initially inspired by the superconvergent patch recovery spr procedure proposed by zienkiewicz and zhu 21,22, have quickly developed and found numerous. The superconvergent patch recovery and aposteriori error. Citeseerx error estimation of navierstokes computations.
This recovery procedure provides statically admissible stress. Sorry, we are unable to provide the full text but you may find it at the following locations. We try to uncover the superconvergent property of virtual element methods by doing some local postprocessing only on the degrees of freedom. In 1992, the superconvergent patch recovery spr method was introduced by zienkiewicz and zhu. Mesh adaptivity driven by goaloriented locally equilibrated superconvergent patch recovery o. Superconvergent patch recovery technique for the finite. Numerical experiments demonstrate that the recovered nodal values of the derivatives with linear and cubic elements are superconvergent. In contrast to that technique all flux or stress components are interpolated at the same time, coupled by equilibrium equations at the superconvergent points. A posteriori error estimation based on the superconvergent. Using linear virtual element method as an example, we propose a universal recovery procedure to improve the accuracy of gradient approximation for numerical methods using general polygonal meshes. This method computes stresses at optimal sampling points where the accuracy of stresses is an order of.
Its implementation is designed for use with most of the numerically integrated 1d, 2d, and 3d elements in the model. Dual techniques are based on the evaluation of two di erent elds, one compatible in displacements and another equilibrated in. The nodal smoothing procedure can be performed using the global l 2 projection, or the superconvergent patch recovery spr. Summary the superconvergent patch recovery spr with bilinear interpolation functions usually gives good values of recovered stresses in an element patch. The superconvergent patch recovery spr and adaptive. It is an extension of the superconvergent patch recovery technique presented by zienkiewicz and zhu. Hence, the quality control of the numerical calculations have to be performed with the. The superconvergence patch recovery technique and data transfer operators in 3d plasticity problems. Pdf mesh adaptivity driven by goaloriented locally. The technique has been tested for a group of widely used linear, quadratic and cubic elements for both one and two dimensional problems. Superconvergent patch recovery spr it is well known that for most elements, certain sampling points exist at which the values of o, have a greater accuracy and.
Read superconvergent patch recovery for plate problems using statically admissible stress resultant fields, international journal for numerical methods in engineering on deepdyve, the largest online rental service for scholarly research with thousands of academic publications available at your fingertips. Even for an unstructured mesh, when adaptive is used, a mesh re nement will usually bring in some kind of structure locally. However, when 4node quadrilateral elements meeting at a node are rigidly rotated with the. Essential ideas and algorithms for implementation of proposed techniques are presented. Center of excellence in structures and earthquake engineering, department of civil engineering, sharif university of technology, p. Superconvergent gradient recovery for virtual element. This work presents a recoverybased error estimation technique for qoi whose main characteristic is the use of an enhanced version of the superconvergent patch recovery spr technique developed by.
Introduction in the socalled superconvergent patch recovery spr method 4, the recovered stress field around a fe node is written oe x. Citeseerx document details isaac councill, lee giles, pradeep teregowda. Abstract for nonlinear problems, it is shown that the accuracy and stability of superconvergent patch recovery spr method can be remarkably improved through the modifications introduced in this. Superconvergent patch recovery for plate problems using statically admissible stress resultant fields. Nonetheless such recovery methods usually deteriorate the convergence properties of linear functionals of the solution and, as a. Modeling of crack propagation via an automatic adaptive.
The proposed technique is called sprcd and provides a recovered displacement field that is then used to obtain. The superconvergent recovery technique developed in the first part of the paper 1 is the used in the computation of the zienkiewiczzhu error estimator to demonstrate accurate estimation of the. The recovery technique used by cgfem is based on the superconvergent patch recovery spr scheme presented and developed in 35, 5860 by zienkiewicz and zhu. The computation of the stiffness matrix and load vectors requires the evaluation of one or more integrals depending on the dimension of the requested analysis. To improve the component of the gradient at a node, an element patch is defined that usually consists of all elements to which the node is connected. Locally equilibrated superconvergent patch recovery for e. On application of two superconvergent recovery procedures. The transfer operators are presented for mapping of the state and internal variables between different meshes. We try to uncover the superconvergent property of the virtual element methods by doing some local postprocessing only on the degrees of freedom.
The implementation of the recovery technique is simple and cost effective. This method is using patch as recovery media as is used by superconvergent patch recovery spr which is. The constructions of cvt and its dual centroidal voronoi delaunay triangulation cvdt are facilitated by a localized lloyd iteration to produce almost equilateral two dimensional meshes. Pdf superconvergent patch recovery for plate problems. Fuenmayor2 november 1, 2018 1institute of mechanics and advanced materials imam, cardi school of engineering, cardi university, queens buildings, the parade, cardi cf24 3aa wales, uk.
The superconvergent patch derivative recovery method of zienkiewicz and zhu is enhanced by adding the squares of the residuals of the equilibrium equation and natural boundary conditions. It is a common belief that the robustness of the zz patch recovery is rooted in its superconvergence property under structured meshes. Pdf rotational dependence of the superconvergent patch. Its implementation is designed for use with most of the numerically integrated 1d, 2. Herein the interior equilibrium is satisfied a priori within each nodal patch. Superconvergence properties of the zz patch recovery are proved in 21 for all popular. The procedure can be classified as superconvergent patch recovery spr enhanced with approximate satisfaction of the interior equilibrium and the natural boundary conditions. The superconvergence patch recovery technique and data. Superconvergence behavior matches well with the use of recovery based a posteriori estimator in the superconvergent patch recovery. Analysis of the superconvergent patch recovery technique. Error estimation based on superconvergent patch recovery. Several a posteriori recovery procedures have been developed over the years to improve the accuracy of postprocessed results. Since the superconvergent patch scp recovery method is relativity easy to understand and is accurate for a wide range of problems, it was selected for implementation in the educational program model.
A specific procedure for recovery of an improved stress field is then developed. Department of structural mechanics, chalmers university of technology, s. For nonlinear problems, it is shown that the accuracy and stability of superconvergent patch recovery spr method can be remarkably improved through the modifications introduced in this paper. An improved superconvergent patch recovery technique for. In this technique, a continuous and accurate stress is obtained over the entire domain by the recovery. The superconvergent cluster recovery method request pdf. Threedimensional superconvergent patch recovery method.
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