A variational multiscale a-posteriori error estimation method for nearly incompressible elasticity

Mixed methods;Multiscale formulation;Stabilized finite elements;A posteriori error estimation;Residual-based estimators

Truster, Timothy J. ; Masud ; Arif

关键词: Mixed methods;    Multiscale formulation;    Stabilized finite elements;    A posteriori error estimation;    Residual-based estimators;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/15985/Truster_Timothy.pdf?sequence=2&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

This work presents an error estimation framework for a mixed displacement-pressure finite element method for nearly incompressible elasticity that is based on variational multiscale concepts. The displacement field is decomposed into coarse scales captured by the finite element mesh and fine scales representing the part of the physics unresolved by the mesh. This solution field decomposition addresses the artificial length scales resulting from discretization of a continuum problem at the variational level to produce a stabilized method equipped with naturally derived error estimators. Two error estimators are proposed. The first employs a representation by bubble functions that arises consistently during the development of the stabilized method and is computed by a simple, direct post-solution evaluation. The second involves solving the fine scale error equation through localization to overlapping patches spread across the domain. The performance of the stabilized method and the error estimators is investigated through numerical convergence tests conducted for two model problems on uniform and distorted meshes. The sharpness and robustness of the estimators is observed to be consistent across the simulations performed.