Improved $P_1$-interpolation error estimates in $W^{1,p}(]0,1[)$: Application to finite element method

Joel Chaskalovic; Franck Assous

paper

Improved $P_{1}$ -interpolation error estimates in $W^{1, p} (] 0, 1 [)$ : Application to finite element method

arXiv:2310.19639

Abstract

Based on a new Taylor-like formula, we derived an improved interpolation error estimate in $W^{1, p}$ . We compare it with the classical error estimates based on the standard Taylor formula, and also with the corresponding interpolation error estimate, derived from the mean value theorem. We then assess the improvement in accuracy we can get from this formula, leading to a significant reduction in finite element computation costs.

17 pages

Improved P1​-interpolation error estimates in W1,p(]0,1[): Application to finite element method

Abstract

Improved $P_{1}$ -interpolation error estimates in $W^{1, p} (] 0, 1 [)$ : Application to finite element method