Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  deals with a posteriori error estimators for the non conforming Crouzeix-Raviart finite element approximations of the Steklov eigenvalue problem. First,  define an error estimator of the residual type which can be computed locally from the approximate eigenpair and  prove the equivalence beten this estimator and the broken energy norm of the error with constants independent of the corresponding eigenvalue. Next,  prove that edge residuals dominate the volumetric part of the residual and that the volumetric part of the residual terms dominate the normal component of the jumps of the discrete fluxes across interior edges. Finally, based on these results,  introduce two simpler equivalent error estimators. The analysis shows that these a posteriori error estimates are optimal up to higher order terms and that may be used for the design of adaptive algorithms.
['Anahí Dello Russo', 'Ana E. Alonso']
I am writing a research paper on a idea A posteriori error estimates for nonconforming approximations of Steklov eigenvalue problems
[{"from": "human", "value": "I am writing a research paper on a idea A posteriori error estimates for nonconforming approximations of Steklov eigenvalue problems"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  deals with a posteriori error estimators for the non conforming Crouzeix-Raviart finite element approximations of the Steklov eigenvalue problem. First,  define an error estimator of the residual type which can be computed locally from the approximate eigenpair and  prove the equivalence beten this estimator and the broken energy norm of the error with constants independent of the corresponding eigenvalue. Next,  prove that edge residuals dominate the volumetric part of the residual and that the volumetric part of the residual terms dominate the normal component of the jumps of the discrete fluxes across interior edges. Finally, based on these results,  introduce two simpler equivalent error estimators. The analysis shows that these a posteriori error estimates are optimal up to higher order terms and that may be used for the design of adaptive algorithms."}]