AN ADAPTIVE-CONTROL OF SPATIAL-TEMPORAL DISCRETIZATION ERROR IN FINITE-ELEMENT ANALYSIS OF DYNAMIC PROBLEMS

The application of adaptive finite element method to dynamic problems is investigated. Both the kinetic and strain energy errors induced by space and time discretization were estimated in a consistent manner an d controlled by the simultaneous use of the adaptive mesh generation a nd the automatic time stepping. Also an optimal ratio of spatial discr etization error to temporal discretization error was discussed. In thi s study it was found that the best performance can be obtained when th e specified spatial and temporal discretization errors have the same v alue. Numerical examples are carried out to verify the performance of the procedure.