A practical algorithm to minimize the overall error in FEM computations

02/05/2022

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by   Jie Liu, et al.

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Using the standard finite element method (FEM) to solve general partial differential equations, the round-off error is found to be proportional to N^β_ R, with N the number of degrees of freedom (DoFs) and β_ R a coefficient. A method which uses a few cheap numerical experiments is proposed to determine the coefficient of proportionality and β_ R in various space dimensions and FEM packages. Using the coefficients obtained above, the strategy put forward in <cit.> for predicting the highest achievable accuracy E_ min and the associated optimal number of DoFs N_ opt for specific problems is extended to general problems. This strategy allows predicting E_ min accurately for general problems, with the CPU time for obtaining the solution with the highest accuracy E_ min typically reduced by 60%–90%.