ADMOS 2025

Error estimation based on local hybrid H1 reconstruction

  • Devloo, Philippe (UNICAMP)
  • Avancini, Giovane (UNICAMP)
  • Shauer, Nathan (UNICAMP)

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In this research we present an error estimator for H1 finite element approximations using a locally constructed hybrid H1 approximation as a basis for the energy error estimator. A theorem similar to the Prager-Synge theorem is derived, but applied to the difference of an H1 and hybrid H1 approximation. Under certain conditions, it can be shown that the difference between both approximations is larger than the error of either the H1 or the hybrid H1 approximation. The advantage of the proposed error estimator is that it requires only the availability of high-order H1 approximations. At first, the potential of the approach is demonstrated by taking the difference of H1 and hybrid H1 approximations and numerically computing the effectivity index. Secondly, a variational statement is derived which allows to reconstruct a hybrid H1 solution using local reconstruction, similarly to the reconstruction of a locally conservative H(div) reconstruction. Finally the effectivity index of the reconstucted approximation is demonstrated by estimating the error with local reconstruction for a range of relevant problems.