## Some optimal error estimates for piecewise linear finite element approximations

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- by Rolf Rannacher and Ridgway Scott PDF
- Math. Comp.
**38**(1982), 437-445 Request permission

## Abstract:

It is shown that the Ritz projection onto spaces of piecewise linear finite elements is bounded in the Sobolev space, $\hat {W}_p^1$, for $2 \leqslant p \leqslant \infty$. This implies that for functions in $\hat {W}_p^1 \cap W_p^2$ the error in approximation behaves like $O(h)$ in $W_p^1$, for $2 \leqslant p \leqslant \infty$, and like $O({h^2})$ in ${L_p}$, for $2 \leqslant p < \infty$. In all these cases the additional logarithmic factor previously included in error estimates for linear finite elements does not occur.## References

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## Additional Information

- © Copyright 1982 American Mathematical Society
- Journal: Math. Comp.
**38**(1982), 437-445 - MSC: Primary 65N30
- DOI: https://doi.org/10.1090/S0025-5718-1982-0645661-4
- MathSciNet review: 645661