A unified framework for the computational comparison of adaptive mesh refinement strategies for all-quadrilateral and all-hexahedral meshes: Locally adaptive multigrid methods versus h-adaptive methods

This paper provides a detailed comparison in solids mechanics context of adaptive mesh refinement methods for all-quadrilateral and all-hexahedral meshes. The multigrid Local Defect Correction method the well-known hierarchical h-adaptive techniques are placed into generic algorithmic setting an objective numerical comparison. Such is great interest as local AMR approaches from now rarely employed to adaptively solve implicit systems solid mechanics. However they present various interesting features mainly related their intrinsic idea partitioning degrees freedom on different levels. For this study, we rely fully-automatic algorithm providing desired refined directly user-prescribed accuracy. process driven by posteriori error estimator combined optimality criteria. In most efficient strategy based criterion ratio identified finite elements quality meshes finally appreciated term number nodes but also through verification final solution's A special attention devoted fulfillment precisions which importance engineering point view. Numerical 2D 3D experiments complexities revealing phenomena enable highlight essential considered within elastostatic framework. study points out potentialities locally method, clearly appears be powerful terms standard metrics efficiency (dimension solved, storage requirements, CPU time).