Postprocessing techniques and h-adaptive finite element-eigenproblem analysis

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.