In this paper, we define a new nonconforming quadrilateral finite element based on the nonconforming rotated Q1 element by enforcing a constraint on each element, which has only three degrees of freedom. We investigat...In this paper, we define a new nonconforming quadrilateral finite element based on the nonconforming rotated Q1 element by enforcing a constraint on each element, which has only three degrees of freedom. We investigate the consistency, approximation, superclose property, discrete Green＇s function and superconvergence of this element. Moreover, we propose a new postprocessing technique and apply it to this element. It is proved that the postprocessed discrete solution is superconvergent under a mild assumption on the mesh.展开更多
Presents information on a study which proposed a mortar element version for rotated Q1 element. Introduction of the model problem; Auxiliary technical lemmas necessary to prove the results; Error estimate.
In this paper, we extend two rectangular elements for Reissner-Mindlin plate [9] to the quadrilateral case. Optimal H and L error bounds independent of the plate hickness are derived under a mild assumption on the mes...In this paper, we extend two rectangular elements for Reissner-Mindlin plate [9] to the quadrilateral case. Optimal H and L error bounds independent of the plate hickness are derived under a mild assumption on the mesh partition.展开更多
This is the third part of the paper for the rotated Q1 nonconforming element on quadrilateral meshes for general second order elliptic problems. Some optimal numerical formulas are presented and analyzed. The novelty ...This is the third part of the paper for the rotated Q1 nonconforming element on quadrilateral meshes for general second order elliptic problems. Some optimal numerical formulas are presented and analyzed. The novelty is that it includes a formula with only two sampling points which excludes even a Q1 unisolvent set. It is the optimal numerical integration formula over a quadrilateral mesh with least sampling points up to now.展开更多
This is the second part of the paper for the mathematical study of nonconforming rotated Q1 element (NRQ1 hereafter) on arbitrary quadrilateral meshes. Some Poincare Inequalities are proved without assuming the quasi-...This is the second part of the paper for the mathematical study of nonconforming rotated Q1 element (NRQ1 hereafter) on arbitrary quadrilateral meshes. Some Poincare Inequalities are proved without assuming the quasi-uniformity of the mesh subdivision. A discrete trace inequality is also proved.展开更多
This paper generalizes two nonconforming rectangular elements of the Reissner-Mindlin plate to the quadrilateral mesh. The first quadrilateral element uses the usual conforming bilinear element to approximate both com...This paper generalizes two nonconforming rectangular elements of the Reissner-Mindlin plate to the quadrilateral mesh. The first quadrilateral element uses the usual conforming bilinear element to approximate both components of the rotation, and the modified nonconforming rotated Q1 element enriched with the intersected term on each element to approximate the displacement, whereas the second one uses the enriched modified nonconforming rotated Q1 element to approximate both the rotation and the displacement. Both elements employ a more complicated shear force space to overcome the shear force locking, which will be described in detail in the introduction. We prove that both methods converge at optimal rates uniformly in the plate thickness t and the mesh distortion parameter in both the H1-and the L2-norms, and consequently they are locking free.展开更多
文摘In this paper, we define a new nonconforming quadrilateral finite element based on the nonconforming rotated Q1 element by enforcing a constraint on each element, which has only three degrees of freedom. We investigate the consistency, approximation, superclose property, discrete Green＇s function and superconvergence of this element. Moreover, we propose a new postprocessing technique and apply it to this element. It is proved that the postprocessed discrete solution is superconvergent under a mild assumption on the mesh.
基金Subsidized by the National Natural Science Foundation of China under Grant 19901014 the Special Funds for Major State Basic Research Projects.
文摘Presents information on a study which proposed a mortar element version for rotated Q1 element. Introduction of the model problem; Auxiliary technical lemmas necessary to prove the results; Error estimate.
基金Subsidized by the Special Funds for Major State Basic Research Projects G1999032804.
文摘In this paper, we extend two rectangular elements for Reissner-Mindlin plate [9] to the quadrilateral case. Optimal H and L error bounds independent of the plate hickness are derived under a mild assumption on the mesh partition.
基金The work of P.-B Ming was partially supported by the National Natural Science Foundation of China 10201033
文摘This is the third part of the paper for the rotated Q1 nonconforming element on quadrilateral meshes for general second order elliptic problems. Some optimal numerical formulas are presented and analyzed. The novelty is that it includes a formula with only two sampling points which excludes even a Q1 unisolvent set. It is the optimal numerical integration formula over a quadrilateral mesh with least sampling points up to now.
基金The work of P.-B.Ming was partially supported by the National Natural Science Foundation of China 10201033
文摘This is the second part of the paper for the mathematical study of nonconforming rotated Q1 element (NRQ1 hereafter) on arbitrary quadrilateral meshes. Some Poincare Inequalities are proved without assuming the quasi-uniformity of the mesh subdivision. A discrete trace inequality is also proved.
基金the National Natural Science Foundation of China (Grant No. 10601003)National Excellent Doctoral Dissertation of China (Grant No. 200718)
文摘This paper generalizes two nonconforming rectangular elements of the Reissner-Mindlin plate to the quadrilateral mesh. The first quadrilateral element uses the usual conforming bilinear element to approximate both components of the rotation, and the modified nonconforming rotated Q1 element enriched with the intersected term on each element to approximate the displacement, whereas the second one uses the enriched modified nonconforming rotated Q1 element to approximate both the rotation and the displacement. Both elements employ a more complicated shear force space to overcome the shear force locking, which will be described in detail in the introduction. We prove that both methods converge at optimal rates uniformly in the plate thickness t and the mesh distortion parameter in both the H1-and the L2-norms, and consequently they are locking free.
