@misc{mosler_an_errorestimatefree_2009, author={Mosler, J., Ortiz, M.}, title={An error-estimate-free and remapping-free variational mesh refinement and coarsening method for dissipative solids at finite strains}, year={2009}, howpublished = {journal article}, doi = {https://doi.org/10.1002/nme.2428}, abstract = {strategy is to refine (respectively, unrefine) the spatial discretization locally if such refinement (respectively, unrefinement) results in a sufficiently large reduction (respectively, sufficiently small increase) in the energy. This strategy leads to an adaption algorithm having O(N) complexity. Local refinement is effected by edge-bisection and local unrefinement by the deletion of terminal vertices. Dissipation is accounted for within a time-discretized variational framework resulting in an incremental potential energy. In addition, the entire hierarchy of successive refinements is stored and the internal state of parent elements is updated so that no mesh-transfer operator is required upon unrefinement. The versatility and robustness of the resulting variational adaptive finite element formulation is illustrated by means of selected numerical examples.}, note = {Online available at: \url{https://doi.org/10.1002/nme.2428} (DOI). Mosler, J.; Ortiz, M.: An error-estimate-free and remapping-free variational mesh refinement and coarsening method for dissipative solids at finite strains. International Journal for Numerical Methods in Engineering. 2009. vol. 77, no. 3, 437-450. DOI: 10.1002/nme.2428}}