A priori error estimates for a Hybrid High-Order method on variable-exponent Leray-Lions problems
Abstract
We derive a priori error estimates for the Hybrid High-Order (HHO) discretization of variable-exponent Leray--Lions problems introduced in a companion convergence study. HHO methods belong to the family of hybrid nonconforming methods, based on cell and face polynomial unknowns of arbitrary degree. Under additional broken regularity of the exact solution and its flux, we establish a localized error estimate that retains the individual element sizes and a global estimate whose rate distinguishes the purely subquadratic, mixed subquadratic--superquadratic, and purely superquadratic regimes. In the subquadratic range, we also derive a regime-dependent refinement that compares the local approximation scale with the local non-degeneracy scale and recovers the optimal polynomial order when that scale is resolved by the mesh. The analysis relies on variable-exponent approximation properties of polynomial projectors, mean-exponent tools for discrete polynomial spaces, and weighted monotonicity estimates. The framework also covers regularized and mildly non-symmetric anisotropic Carreau--Yasuda-type fluxes. Numerical experiments on Cartesian and Voronoi meshes support the predicted rates and show that the regularity assumption on the flux cannot be dispensed with.
Related
- A Hybrid High-Order method for variable-exponent Leray-Lions problems with convergence under minimal regularity
- Multiplicity of weak solutions for mixed variable exponent triharmonic problems with hardy potentials
- A Priori and A Posteriori Error Estimates for a Crank Nicolson Type Scheme of an Elliptic Problem with Dynamical Boundary Conditions
- A priori bounds for geodesic diameter. Part III. A Sobolev–Poincaré inequality and applications to a variety of geometric variational problems
- A Priori Estimates for Singular Fractional Stochastic Burgers Equations
BibTeX
@misc{harnist2026priori,
title = {{A priori error estimates for a Hybrid High-Order method on variable-exponent Leray-Lions problems}},
author = {André Harnist and Romain Mottier},
howpublished = {HAL},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.21611},
eprint = {2610.21611},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05801004v1},
}
RIS
TY - UNPB
TI - A priori error estimates for a Hybrid High-Order method on variable-exponent Leray-Lions problems
AU - André Harnist
AU - Romain Mottier
PY - 2026
DA - 2026/10/15
PB - HAL
DO - 10.48550/arxiv.2610.21611
UR - https://hal.science/hal-05801004v1
AB - We derive a priori error estimates for the Hybrid High-Order (HHO) discretization of variable-exponent Leray--Lions problems introduced in a companion convergence study. HHO methods belong to the family of hybrid nonconforming methods, based on cell and face polynomial unknowns of arbitrary degree. Under additional broken regularity of the exact solution and its flux, we establish a localized error estimate that retains the individual element sizes and a global estimate whose rate distinguishes the purely subquadratic, mixed subquadratic--superquadratic, and purely superquadratic regimes. In the subquadratic range, we also derive a regime-dependent refinement that compares the local approximation scale with the local non-degeneracy scale and recovers the optimal polynomial order when that scale is resolved by the mesh. The analysis relies on variable-exponent approximation properties of polynomial projectors, mean-exponent tools for discrete polynomial spaces, and weighted monotonicity estimates. The framework also covers regularized and mildly non-symmetric anisotropic Carreau--Yasuda-type fluxes. Numerical experiments on Cartesian and Voronoi meshes support the predicted rates and show that the regularity assumption on the flux cannot be dispensed with.
ER -