Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A new recovery technique explicit polynomial recovery (EPR) is analyzed for finite element methods. EPR reconstructs the value at edge centers by solving a local problem. In combination with the finite element solution at the vertex, a quadratic approximation is constructed. Besides improving the accuracy, it can also be applied in building the EPR-based error estimator. For the Poisson equation, the element center is a superconvergent point of the gradient of the EPR recovered function on an equilateral triangulation. Numerical examples are presented to verify the theoretical results and to show the performance of the EPR in the adaptive finite element method.
['Yunqing Huang', 'Wei Yang', 'Nianyu Yi']
I am writing a research paper on a idea Superconvergence analysis for the explicit polynomial recovery method
[{"from": "human", "value": "I am writing a research paper on a idea Superconvergence analysis for the explicit polynomial recovery method"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A new recovery technique explicit polynomial recovery (EPR) is analyzed for finite element methods. EPR reconstructs the value at edge centers by solving a local problem. In combination with the finite element solution at the vertex, a quadratic approximation is constructed. Besides improving the accuracy, it can also be applied in building the EPR-based error estimator. For the Poisson equation, the element center is a superconvergent point of the gradient of the EPR recovered function on an equilateral triangulation. Numerical examples are presented to verify the theoretical results and to show the performance of the EPR in the adaptive finite element method."}]