Numerical construction of optimal adaptive grids in two spatial dimensions

Chen, Tsu-Fen; Yang, H. D.

doi:10.1016/s0898-1221(00)00133-4

Cited by 13 publications

(18 citation statements)

References 14 publications

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“…Monitor functions are used by many authors (see, e.g., [4][5][6][7]9,12,18,20]) to drive adaptive algorithms that produce layer-resolving meshes in solving differential equations. We first give a general description of this methodology, then use the theoretical results of section 3 to choose monitor functions that are appropriate for (1.1).…”

Section: Monitor Functionsmentioning

confidence: 99%

Grid equidistribution for reaction–diffusion problems in one dimension

2005

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The numerical solution of a linear singularly-perturbed reaction-diffusion two-point boundary value problem is considered. The method used is adaptive movement of a fixed number of mesh points by monitor-function equidistribution. A partly heuristic argument based on truncation error analysis leads to several suitable monitor functions, but also shows that the standard arc-length monitor function is unsuitable for this problem. Numerical results are provided to demonstrate the effectiveness of our preferred monitor function.

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Section: Monitor Functionsmentioning

confidence: 99%

Grid equidistribution for reaction–diffusion problems in one dimension

2005

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“…Using the grading function derived in [2], based on finite element approximations, a mesh redistribution algorithm in two spatial dimensions was developed and applied to convection-diffusion problems by Chen and Yang in [8]. The algorithm extended a one dimensional equidistribution principle to minimize the interpolation error in appropriate norms.…”

Section: Introductionmentioning

confidence: 99%

“…The final grids generated were connected by an unstructured grid generation technique considered in [9]. In this paper, the algorithm in [8] will be modified for optimal grids construction in the least-squares approximations. Note that optimal convergence can be achieved in the least-squares approximations if the triangular mesh satisfies the grid decomposition property [10].…”

Section: Introductionmentioning

confidence: 99%

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Optimal adaptive grids of least-squares finite element methods in two spatial dimensions

Chang

Chen

2011

Journal of Computational and Applied Mathematics

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a b s t r a c tThis article concerns a procedure to generate optimal adaptive grids for convection dominated problems in two spatial dimensions based on least-squares finite element approximations. The procedure extends a one dimensional equidistribution principle which minimizes the interpolation error in some norms. The idea is to select two directions which can reflect the physics of the problems and then apply the one dimensional equidistribution principle to the chosen directions. Model problems considered are the two dimensional convection-diffusion problems where boundary and interior layers occur. Numerical results of model problems illustrating the efficiency of the proposed scheme are presented. In addition, to avoid skewed mesh in the optimal grids generated by the algorithm, an unstructured local mesh smoothing will be considered in the leastsquares approximations. Comparisons with the Gakerkin finite element method will also be provided.

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“…The concept of equidisbribution mesh is to map a set of irregular distributed nodes in the physical domain to a regular grid point in the computational non-dimensional domain by using a monitor function. For its implementations, most of them emphasize solving one-and two-dimensional differential equations [4][5][6][7]. Some researches have analyzed elasto-static problems by using the boundary element method [8][9][10].…”

Section: Introductionmentioning

confidence: 99%

Relative-Error-Based Finite Element Analysis of Axially Moving Beams

Kuo

Cleghorn

Behdinan

2006

Transactions of the Canadian Society for Mechanical Engineering

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The r-refinement increases accuracy of finite element solutions, but not increases computations. This paper presents a new and efficient technique applied to the r-refinement, which is based on the relative errors. This technique does not need a reference solution, and any physical quantity, such as energy, displacement, stress, etc., can be arbitrarily selected and applied to this technique. A simple algorithm is provided to find the optimum positions of nodes instead of solving a variety of nonlinear equations. Furthermore, this paper demonstrates this technique and provides a comprehensive finite element analysis of flexible axially moving beam by using the h-, p-and r-refinements. lIL'ERREUR RELATIVE A BASE lI L'ANALYSE D'ELEMENT FINIE DE DEPLACER AXIALEMENT DES BIELLESLe r-raffinement augmente l'exactitude de solutions d'eh\ment finies, mais pas comptes d'augmentations. Ces presents de papier une technique nouvelle et efficace s'est appliquee au r-raffinement, qui est fonde sur les erreurs relatives. Cette technique n'a pas besoin d'nne solution de reference et n'importe quelle quantite physique, comme l'energie, Ie deplacement, la tension, etc., peut arbitrarily choisi et s'est appliquee it cette technique. Un algorithme simple est foumi pour trouver les positions optimales de noeuds au lieu de resoudre une variete d'equations non lineaires. En outre, ce papier demontre cette technique et foumit une analyse d'element finie complete de bielle flexible axialement bougeante en utilisant Ie h-, poet les r-raffinements.

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Numerical construction of optimal adaptive grids in two spatial dimensions

Cited by 13 publications

References 14 publications

Grid equidistribution for reaction–diffusion problems in one dimension

Grid equidistribution for reaction–diffusion problems in one dimension

Optimal adaptive grids of least-squares finite element methods in two spatial dimensions

Relative-Error-Based Finite Element Analysis of Axially Moving Beams

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