An a priori L2–norm error estimate of the hybrid high-order method for a class of strongly monotone nonlinear elliptic problems

Bustinza R.; Munguia-La-Cotera J. · Advances in Computational Mathematics (2026) · DOI: 10.1007/s10444-026-10329-0

Resumen

In this paper, we apply the already known hybrid high-order (HHO) method to solve a certain class of strongly monotone nonlinear elliptic problems. We prove the well-posedness of the discrete formulation and obtain the expected rates of convergence in the energy norm. Concerning the convergence in the L2 norm, we notice that, at least pre-asymptotically, one could observe an optimal rate of convergence on coarse enough meshes. The strategy relies on a duality argument and a technical result that mimics a mean value type property for vector-valued functions. Up to the author’s knowledge, this kind of result has not been proven before for nonlinear elliptic problems. Several computational experiments give us numerical evidence that our L2-norm error estimate could be improved. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2026.

Instituciones: Universidad Nacional de Ingeniería