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Keywords: finite element method, 3D hp autoadaptive method, error estimation, object oriented programming, elasticity, fluid mechanics.

Summary

An autoadaptive strategy is presented which uses a local a-posteriori error estimator. The refinement criteria uses the results of the a-posteriori error estimator to decide on h- and/or h-p refinement and is based on regularity analysis of one dimensional problems along the edges of the elements.

The autoadaptive refinement procedure is generic and is applied to several types of finite element simulations. It is also independent of the dimension of the problem. The proposed algorithm is implemented using the PZ environment, an object oriented framework to develop finite element simulations. The analyzed problems presented exponential convergence rates, even for singular problems. This paper emphasizes the qualification of the correctness of the implemented hp-autoadaptive finite elements and the illustration of its application to a variety of problems.

The qualification of the program includes the necessary steps to ensure the results of the hp-adaptive finite element program are reliable. The tests proposed maybe useful to authors implementing hp-adaptive finite element software.

The validation is divided by the dimension of the problem. For each dimension, the same mesh is first solved using a mesh with homogeneous element types. Then the same solution is approximated with several element types. For example, a bi-dimensional problem is solved using a triangle element based mesh, a quad element based mesh and finally using an mixed element mesh.

For tri-dimensional problems we use an hexahedre element based mesh as homogeneous mesh and the heterogeneous mesh uses a mix of prism, pyramid and tetrahedra elements.

Two types of singularities are imposed in bi-dimensional model: geometric singularities (L corner) and model equation singularities. For three dimensional problems only model equation singularities were simulated.

Results are presented for thermal diffusion on 2D and 3D meshes. Each problem is solved using homogeneous element meshes and heterogeneous element meshes for comparison purposes. The effectivity index of the a-posteriori error estimator is computed for problems where an analytic solution is available.

The sample problems include points and/or lines of singularity and allow to verify the effectiveness of the hp-autoadaptive algorithms.

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Front Page Browse CCP CSETS CTR IJRT Other Authors Search Purchase Guide FAQ Contact us	Civil-Comp Proceedings ISSN 1759-3433 CCP: 77 PROCEEDINGS OF THE NINTH INTERNATIONAL CONFERENCE ON CIVIL AND STRUCTURAL ENGINEERING COMPUTING Edited by: B.H.V. Topping Paper 22 hp Auto Adaptive Finite Element Method on 3D Heterogeneous Meshes P.R.B Devloo, C.M.A.A. Bravo and E.C. Rylo College of Civil Engineering, University of Campinas - UNICAMP, Brazil doi:10.4203/ccp.77.22 purchase the full-text of this paper Full Bibliographic Reference for this paper P.R.B Devloo, C.M.A.A. Bravo, E.C. Rylo, "hp Auto Adaptive Finite Element Method on 3D Heterogeneous Meshes", in B.H.V. Topping, (Editor), "Proceedings of the Ninth International Conference on Civil and Structural Engineering Computing", Civil-Comp Press, Stirlingshire, UK, Paper 22, 2003. doi:10.4203/ccp.77.22 Keywords: finite element method, 3D hp autoadaptive method, error estimation, object oriented programming, elasticity, fluid mechanics. Summary An autoadaptive strategy is presented which uses a local a-posteriori error estimator. The refinement criteria uses the results of the a-posteriori error estimator to decide on h- and/or h-p refinement and is based on regularity analysis of one dimensional problems along the edges of the elements. The autoadaptive refinement procedure is generic and is applied to several types of finite element simulations. It is also independent of the dimension of the problem. The proposed algorithm is implemented using the PZ environment, an object oriented framework to develop finite element simulations. The analyzed problems presented exponential convergence rates, even for singular problems. This paper emphasizes the qualification of the correctness of the implemented hp-autoadaptive finite elements and the illustration of its application to a variety of problems. The qualification of the program includes the necessary steps to ensure the results of the hp-adaptive finite element program are reliable. The tests proposed maybe useful to authors implementing hp-adaptive finite element software. The validation is divided by the dimension of the problem. For each dimension, the same mesh is first solved using a mesh with homogeneous element types. Then the same solution is approximated with several element types. For example, a bi-dimensional problem is solved using a triangle element based mesh, a quad element based mesh and finally using an mixed element mesh. For tri-dimensional problems we use an hexahedre element based mesh as homogeneous mesh and the heterogeneous mesh uses a mix of prism, pyramid and tetrahedra elements. Two types of singularities are imposed in bi-dimensional model: geometric singularities (L corner) and model equation singularities. For three dimensional problems only model equation singularities were simulated. Results are presented for thermal diffusion on 2D and 3D meshes. Each problem is solved using homogeneous element meshes and heterogeneous element meshes for comparison purposes. The effectivity index of the a-posteriori error estimator is computed for problems where an analytic solution is available. The sample problems include points and/or lines of singularity and allow to verify the effectiveness of the hp-autoadaptive algorithms. purchase the full-text of this paper (price £20) go to the previous paper go to the next paper return to the table of contents return to the book description purchase this book (price £123 +P&P)
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