The generic h-adaptive procedure consists in the appropriate combination of the following components: (i) finite element solver for the problem under consideration, (ii) reliable posteriori error estimator providing a measure of the local error in a given norm to locate the regions that should be subjected to (de)refinement, (iii) refinement strategy translating the output from the error analysis into the desired distribution of mesh density, (iv) mesh generator capable of (de)refinement according to the supplied mesh density distribution, and (v) mapping operator which projects the current state of the model from the old mesh to the new (adapted) one. 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.

*Daniel Rypl
2005-12-03*