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Generally finite element mesh generation work is well established for homogenous objects where object-geometry is the main criteria for meshing an object. The effect of variation of material property as happens in case of FGMs, on...
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Generally finite element mesh generation work is well established for homogenous objects where object-geometry is the main criteria for meshing an object. The effect of variation of material property as happens in case of FGMs, on mesh size is largely remains untouched. Present work considers the elastic property gradient as criteria for meshing and studies its impact on the convergence of the analysis result. A one dimensional functionally graded bar was considered, and the meshing is done for different elastic modulus variation within the bar. It was observed that elastic gradient basis for element size will have positive effect on convergence if a different gradient relationship is chosen for the meshing. The relationship between the elastic property variation function and the mesh size variation function was established. It was observed that for an optimum convergence result, the gradient power taken for meshing is in general different from the power that represents the material property variation. This work is a unique and is expected to have significant in improvement in the finite element meshing and convergence of FGM.
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We present a practical approach to isotropic tetrahedral meshing of 3D domains bounded by piecewise smooth surfaces. Building upon recent theoretical and practical advances, our algorithm interleaves Delaunay refinement and mesh o...
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We present a practical approach to isotropic tetrahedral meshing of 3D domains bounded by piecewise smooth surfaces. Building upon recent theoretical and practical advances, our algorithm interleaves Delaunay refinement and mesh optimization to generate quality meshes that satisfy a set of user-defined criteria. This interleaving is shown to be more conservative in number of Steiner point insertions than refinement alone, and to produce higher quality meshes than optimization alone. A careful treatment of boundaries and their features is presented, offering a versatile framework for designing smoothly graded tetrahedral meshes.
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To achieve the exponential rates of convergence possible with the p-version finite element method requires properly constructed meshes. In the case of piecewise smooth domains, these meshes are characterized by having large curved...
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To achieve the exponential rates of convergence possible with the p-version finite element method requires properly constructed meshes. In the case of piecewise smooth domains, these meshes are characterized by having large curved elements over smooth portions of the domain and geometrically graded curved elements to isolate the edge and vertex singularities that are of interest. This paper presents a procedure under development for the automatic generation of such meshes for general three-dimensional domains defined in solid modeling systems. Two key steps in the procedure are the determination of the singular model edges and vertices, and the creation of geometrically graded elements around those entities. The other key step is the use of general curved element mesh modification procedures to correct any invalid elements created by the curving of mesh entities on the model boundary, which is required to ensure a properly geometric approximation of the domain. Example meshes are included to demonstrate the features of the procedure.
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We study the approximation properties of some general finite-element spaces constructed using improved graded meshes. In our results, either the approximating function or the function to be approximated (or both) are in a weighted...
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We study the approximation properties of some general finite-element spaces constructed using improved graded meshes. In our results, either the approximating function or the function to be approximated (or both) are in a weighted Sobolev space. We consider also the L-p-version of these spaces. The finite-element spaces that we define are obtained from conformally invariant families of finite elements (no affine invariance is used), stressing the use of elements that lead to higher regularity finite-element spaces. We prove that for a suitable grading of the meshes, one obtains the usual optimal approximation results. We provide a construction of these spaces that does not lead to long, "skinny" triangles. Our results are then used to obtain L-2-error estimates and h(m)-quasi-optimal rates of convergence for the FEM approximation of solutions of strongly elliptic interface/boundary value problems.
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Background: Currently, >200 meshes are commercially available in the United States. To help guide appropriate mesh selection, the investigators examined the postsurgical experiences of all patients undergoing ventral hernia repair...
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Background: Currently, >200 meshes are commercially available in the United States. To help guide appropriate mesh selection, the investigators examined the postsurgical experiences of all patients undergoing ventral hernia repair at their facility from 2008 to 2011 with ≥12 months of follow-up. Methods: A retrospective review of prospectively collected data was conducted. All returns (surgical readmission, office or emergency visit) for complications or recurrences were examined. The impact of demographics (age, gender, and body mass index [BMI]), risk factors (hernia grade, hernia size, concurrent and past bariatric surgery, concurrent and past organ transplantation, any concurrent surgery, and American Society of Anesthesiologists score), and prosthetic type (polypropylene, other synthetic, human acellular dermal matrix, non-cross-linked porcine-derived acellular dermal matrix, other biologic, or none) on the frequency of return was evaluated. Results: A total of 564 patients had 12 months of follow-up, and 417 patients had 18 months of follow-up. In a univariate regression analysis, study arm (biologic, synthetic, or primary repair), hernia grade, hernia size, past bariatric surgery, and American Society of Anesthesiologists score were significant predictors of recurrence (P <.05). Multivariate analysis, stepwise regression, and interaction tests identified three variables with significant predictive power: hernia grade, hernia size, and BMI. The adjusted odds ratios vs hernia grade 2 for surgical readmission were 2.6 (95% confidence interval [CI], 1.3 to 5.1) for grade 3 and 2.6 (95% CI, 1.1 to 6.4) for grade 4 at 12 months and 2.3 (95% CI, 1.1 to 4.6) for grade 3 and 4.2 (95% CI, 1.7 to 10.0) for grade 4 at 18 months. Large hernia size (adjusted odds ratio vs small size, 3.2; 95% CI, 1.6 to 6.2) and higher BMI (adjusted odds ratio for BMI ≥50 vs 30 to 34.99 kg/m2, 5.7; 95% CI, 1.2 to 26.2) increased the likelihood of surgical readmission within 12 months. Conclusions: The present data support the hypothesis that careful matching of patient characteristics to choice of prosthetic will minimize complications, readmissions, and the number of postoperative office visits.
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In a paper by R. Duran, A. Lombardi, and the authors (2007) the finite element method was applied to a non-homogeneous Neumann problem on a cuspidal domain Ω ∩ R~2, and quasi-optimal order error estimates in the energy norm were...
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In a paper by R. Duran, A. Lombardi, and the authors (2007) the finite element method was applied to a non-homogeneous Neumann problem on a cuspidal domain Ω ∩ R~2, and quasi-optimal order error estimates in the energy norm were obtained for certain graded meshes. In this paper, we study the error in the L~2 norm obtaining similar results by using graded meshes of the type considered in that paper. Since many classical results in the theory Sobolev spaces do not apply to the domain under consideration, our estimates require a particular duality treatment working on appropriate weighted spaces. On the other hand, since the discrete domain Ω_h verifies Ω ∩ Ω_h, in the above-mentioned paper the source term of the Poisson problem was taken equal to 0 outside Ω in the variational discrete formulation. In this article we also consider the case in which this condition does not hold and obtain more general estimates, which can be useful in different problems, for instance in the study of the effect of numerical integration, or in eigenvalue approximations.
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In this paper we analyze the standard piece-wise bilinear finite element approximation of a model reaction-diffusion problem. We prove supercloseness results when appropriate graded meshes are used. The meshes are those introduced...
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In this paper we analyze the standard piece-wise bilinear finite element approximation of a model reaction-diffusion problem. We prove supercloseness results when appropriate graded meshes are used. The meshes are those introduced in Durán and Lombardi (2005) [8] but with a stronger restriction on the graduation parameter. As a consequence we obtain almost optimal error estimates in the L2-norm thus completing the error analysis given in Durán and Lombardi (2005) [8].
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This paper is concerned with adaptive least-squares methods for Stokes equations based on velocity-pressure-stress and velocity-vorticity-pressure formulations. To capture the Stokes flow region, an adaptive algorithm based on mes...
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This paper is concerned with adaptive least-squares methods for Stokes equations based on velocity-pressure-stress and velocity-vorticity-pressure formulations. To capture the Stokes flow region, an adaptive algorithm based on mesh redistribution is developed for a nonlinear weighted least-squares functional. A redistribution approach is considered to generate the optimal grids. Model problems considered are the flow past a planar channel and a 4-to-1 contraction problems. Numerical results of model problems illustrating the efficiency of the proposed scheme are presented. (C) 2014 Elsevier B.V. All rights reserved.
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The paper deals with Nitsche type mortaring as a finite element method (PEM) for treating non- matching meshes of triangles at the interface of some domain decomposition. The approach is applied to the Poisson equation with Dirich...
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The paper deals with Nitsche type mortaring as a finite element method (PEM) for treating non- matching meshes of triangles at the interface of some domain decomposition. The approach is applied to the Poisson equation with Dirichlet boundary conditions (as a model problem) under the aspect that the interface passes re-entrant corners of the domain. For such problems and non-matching meshes with and without local refinement near the re-entrant corner, some properties of the finite element scheme and error estimates are proved.
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The numerical approximation by a lower-order anisotropic nonconforming finite element on appropriately graded meshes are considered for solving semisingular perturbation problems. The quasi-optimal-order error estimates are proved...
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The numerical approximation by a lower-order anisotropic nonconforming finite element on appropriately graded meshes are considered for solving semisingular perturbation problems. The quasi-optimal-order error estimates are proved in the epsilon-weighted H-1-norm valid uniformly, up to a logarithmic factor, in the singular perturbation parameter. By using the interpolation postprocessing technique, the global superconvergent error estimates in epsilon-weighted H-1-norm are obtained. Numerical experiments are given to demonstrate validity of our theoretical analysis. Copyright (C) 2007 John Wiley & Sons, Ltd.
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