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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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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


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.
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Additional Information
  • © Copyright 1982 American Mathematical Society
  • Journal: Math. Comp. 38 (1982), 437-445
  • MSC: Primary 65N30
  • DOI:
  • MathSciNet review: 645661