Postprocessing techniques and h-adaptive finite element-eigenproblem analysis |
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| Affiliation: | 1. Laboratory of Numerical Modelling, Vilnius Gediminas Technical University, LT-2040 Vilnius, Lithuania;2. Department of Structural Mechanics, Chalmers University of Technology, Sven Hultins gata 8, SE-41296 Goteborg, Sweden;1. Vlerick Business School, Reep 1, 9000 Ghent, Belgium;2. Rotterdam School of Management, Erasmus University Rotterdam, Burgemeester Oudlaan 50, 3062 PA Rotterdam, The Netherlands;3. Ghent University, Tweekerkenstraat 2, 9000 Gent, Belgium;4. KU Leuven, Naamsestraat 69, 3000 Leuven, Belgium;1. School of Plant, Environment and Soil Sciences, Louisiana State University AgCenter, Baton Rouge, LA70803, USA;2. College of Physics and Energy, Fujian Normal University, Fuzhou, Fujian, 350117, China;3. Department of Oceanography and Coastal Sciences, Louisiana State University, Baton Rouge, LA70803, USA;1. Department of Materials Science and Engineering, Novosibirsk State Technical University, Novosibirsk 630073, Russia;2. Budker Institute of Nuclear Physics, Novosibirsk 630090, Russia;3. Synchrotron Radiation Facility SKIF, Boreskov Institute of Catalysis SB RAS, Kol’tsovo 630559, Russia;4. Institute of Strength Physics and Materials Science, Tomsk 634055, Russia;1. The Queen Elizabeth Hospital, Kings Lynn, UK;2. James Paget University Hospital, Great Yarmouth, UK |
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| Abstract: | The paper presents postprocessing techniques based on locally improved finite element (FE) solutions of the basic field variables. This opens up the possibility to control both “strain energy” terms and “kinetic energy” terms in the governing equations. The proposed postprocessing technique on field variables is essentially a least square fit of the prime variables (displacements) at superconvergent points. Its performance is compared with other well-known techniques, showing a good performance. A h-adaptive FE strategy for acoustic problems is presented where, for adaptive mesh generation and remeshing the commercial software package i-deas has been applied and for the FE analysis the commercial software package sysnoise. The paper also presents an adaptive h-version FE approach to control the discretisation error in free vibration analysis. The postprocessing technique used here is a mix of local and global updating methods. Rapid convergence of the preconditioned conjugate gradient method is enhanced by choosing the initial trial eigenmodes as the superconvergent patch recovery technique for displacements improved FE eigenmodes. Numerical examples show nice properties of the final local and global updated solution as a basis for an error estimator and the error indicator in an adaptive process. |
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