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Adaptive Analysis

The generic h-adaptive procedure consists in the appropriate combination of the following components

Initially, the problem is discretized using the mesh generator, optionally taking into account a-priori error assessment (typically based on the user experience). This discretization is then analyzed using the finite element solver. After each step of the nonlinear solution, the error estimation is invoked. If the global relative error exceeds the prescribed value the refinement strategy is applied to create mesh density distribution map which is afterwards used by the mesh generator to produce the next, appropriately (de)refined mesh. The finite element solver is then restarted from the previous step, when the relative error was still below the defined threshold. The solution (primary unknowns as well as the state variables) from this step is mapped on the new mesh, the equilibrium and consistency are recovered and the analysis continues as long as the error remains within the permissible range. This process is repeated until the analysis is completed.

Clearly, the efficiency of such a methodology depends not only on the efficiency of its individual components but also on the way how it is automated to minimize the user intervention.

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Daniel Rypl