Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: By employing the infinite multilevel representation of the residual,  derive computable bounds to estimate the distance of finite element approximations to the solution of the Poisson equation. If the finite element approximation is a Galerkin solution, the derived error estimator coincides with the standard element and edge based estimator. If Galerkin orthogonality is not satisfied, then the discrete residual additionally appears in terms of the BPX preconditioner. As a by-product of the present analysis, conditions are derived such that the hierarchical error estimation is reliable and efficient.
['Helmut Harbrecht', 'Reinhold Schneider']
I am writing a research paper on a idea A Note on Multilevel Based Error Estimation
[{"from": "human", "value": "I am writing a research paper on a idea A Note on Multilevel Based Error Estimation"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: By employing the infinite multilevel representation of\u00a0the residual,  derive computable bounds to estimate\u00a0the distance of finite element approximations to the\u00a0solution of the Poisson equation. If the finite element\u00a0approximation is a Galerkin solution, the derived error\u00a0estimator coincides with the standard element and edge\u00a0based estimator. If Galerkin orthogonality is not satisfied,\u00a0then the discrete residual additionally appears in terms of\u00a0the BPX preconditioner. As a by-product of the present\u00a0analysis, conditions are derived such that the hierarchical\u00a0error estimation is reliable and efficient."}]