A study of adaptively remeshed finite element problems using higher order tetrahedra

Schuetze, K.T.; Shiakolas, Panos S.; Muthukrishnan, S. N.; Nambiar, R.V.; Lawrence, K. L.

doi:10.1016/0045-7949(94)00320-3

Cited by 8 publications

(1 citation statement)

References 7 publications

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“…In equation (16), the second term used is the equilibrium term which is included to increase the accuracy of the recovery stress and the overall stability of the recovery procedure. However, it should be mentioned that the use of the equilibrium term alone may not be possible to eliminate entirely all the unstable cases and therefore a checking procedure is developed to detect cases of ill-conditioning.…”

Section: ¹He Scpr¹ For 3-d Problemsmentioning

confidence: 99%

Automatic Adaptive 3-D Finite Element Refinement Using Different-Order Tetrahedral Elements

Lee

1997

Int. J. Numer. Meth. Engng.

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SUMMARYAutomatic refinement finite element analyses were carried out employing three different-order tetrahedral solid elements for the solution of 3-D stress analysis problems. Numerical results indicated that the adaptive refinement procedure could eliminate effectively the effect of singularities and the optimal convergence rate was achieved in all the examples tested. The preconditioned conjugate gradient technique was used for the solution of the large system of simultaneous equations. By interpolating the initial guess of the iteration solver from the previous converged solution, the number of iterations needed for the solution is lower than expected. Furthermore, when the mesh density distribution pattern has converged, it became even more efficient and independent of the number of degrees of freedom in the finite element mesh. The relative efficiency of the three different-order tetrahedral elements has also been compared in terms of storage and computational cost needed for achieving a certain accuracy. It is found that although the cubic T20 element can achieve the highest convergence rate, the T10 element is the most competitive and effective element in terms of storage and computational cost needed.1997 by John Wiley & Sons, Ltd.

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Section: ¹He Scpr¹ For 3-d Problemsmentioning

confidence: 99%

Automatic Adaptive 3-D Finite Element Refinement Using Different-Order Tetrahedral Elements

Lee

1997

Int. J. Numer. Meth. Engng.

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3D adaptive mesh refinement

Merrouche¹,

Selman²,

Knopf-Lenoir³

1998

Commun. Numer. Meth. Engng.

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SUMMARYAn adaptive ®nite element (FE) method for the solution of three-dimensional elasto-static problems is described. The computational domain is represented by an assembly of tetrahedral elements and the mesh adaptation is achieved by a 3D bisection method using an error estimator procedure coupled with an automatic 3D mesh generator. The performance of the method is demonstrated using a number of examples.

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Pre‐ and post‐processor techniques in finite element methods: A bibliography (1996–1997)

Mackerle

1998

Progress Structural Eng Maths

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This article gives a bibliographical review of the pre‐ and post‐processor techniques applied to finite element methods (FEMs). The following topics are included: pre‐processors — 2‐D and 3‐D mesh generation techniques, adaptive mesh generation, artificial intelligence (Al) in mesh generation, parallel mesh generation; post‐processors — visualization of computed results, animation. An extensive list of more than 350 references is included in the Survey of current literature which follows this article. It includes papers, conference proceedings and theses/dissertations that were published during 1996 and 1997. Some previously published reviews, key papers and books on the subject are also listed.

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A study of adaptively remeshed finite element problems using higher order tetrahedra

Cited by 8 publications

References 7 publications

Automatic Adaptive 3-D Finite Element Refinement Using Different-Order Tetrahedral Elements

Automatic Adaptive 3-D Finite Element Refinement Using Different-Order Tetrahedral Elements

3D adaptive mesh refinement

Pre‐ and post‐processor techniques in finite element methods: A bibliography (1996–1997)

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