Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A conforming finite element method on polygonal meshes is revied which handles hanging nodes naturally. Trial functions are defined to fulfil the homogeneous PDE locally and they are treated by means of local boundary integral equations. Using a quasi-interpolation operator of Clement type a residual-based error estimate is obtained. This a posteriori estimator can be used to rate the accuracy of the approximation over polygonal elements or it can be applied to an adaptive BEM-based FEM. The numerical experiments confirm our results and show optimal convergence for the adaptive strategy on general meshes.
['Steffen Weißer']
I am writing a research paper on a idea Residual error estimate for BEM-based FEM on polygonal meshes
[{"from": "human", "value": "I am writing a research paper on a idea Residual error estimate for BEM-based FEM on polygonal meshes"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A conforming finite element method on polygonal meshes is revied which handles hanging nodes naturally. Trial functions are defined to fulfil the homogeneous PDE locally and they are treated by means of local boundary integral equations. Using a quasi-interpolation operator of Clement type a residual-based error estimate is obtained. This a posteriori estimator can be used to rate the accuracy of the approximation over polygonal elements or it can be applied to an adaptive BEM-based FEM. The numerical experiments confirm our results and show optimal convergence for the adaptive strategy on general meshes."}]