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Comparison of the round-off error line represented by α R,M+ and β R,M to that represented by α R,O and β R,O for the 1D Poisson problem with u = e −(x−0.5) 2 .
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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 $N^{\beta_{\rm R}}$, with $N$ the number of degrees of freedom (DoFs) and $\beta_{\rm R}$ a coefficient. A method which uses a few cheap numerical experiments is proposed to determine the coefficient of...
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... the round-off error line represented by α R,M+ and β R,M is compared to that represented by α R,O and β R,O in Fig. 7(a). In this figure, the solid lines correspond to the round-off error using the OS method, while the dashed lines correspond to the round-off error using the MS+ method; the results for the principle variable u and derivatives u x and u xx are color-coded black, blue, and red, respectively (same below). As can be seen, the two types of ...
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