arXiv subjects

Kirubell B. Haile

Publications and source records attributed to Kirubell B. Haile.

4 recordsLinked to original sources

arXiv2026

A Reynolds-semi-robust H(div)-conforming method for unsteady incompressible power-law flows

In this work, we prove what appear to be the first Reynolds-semi-robust and pressure-robust velocity error estimates for an H(div)-conforming approximation of unsteady incompressible flows of power-law type fluids. The proposed methods hinges on a discontinuous Galerkin approximation of the viscous term and a reinforced upwind-type stabilization of the convective term. The derived velocity error estimates account for pre-asymptotic orders of convergence observed in convection-dominated flows through regime-dependent estimates of the error contributions. A complete set of numerical results validate the theoretical findings.

math.NA↗

arXiv2026

A Mixed Virtual Element Method for the p-Laplace equation

We introduce and analyze a mixed Virtual Element Method for the $p$-Laplace equation in a non-Hilbertian setting, covering the full range $p \in (1, \infty)$. The discrete framework combines standard mixed Virtual Element spaces with a novel non-linear stabilization term designed to mimic the power-law structure of the continuous operator. We establish discrete inf-sup stability under non-Hilbertian norms and rigorously prove the continuity and coercivity of the discrete form. This guarantees the well-posedness of the problem and allows us to derive a priori error estimates for the primal variable and the flux. A set of numerical tests supports the theoretical derivations.

math.NA↗

arXiv2025

A Reynolds-semi-robust method with hybrid velocity and pressure for the unsteady incompressible Navier--Stokes equations

In this paper we propose and analyze a new Finite Element method for the solution of the two- and three-dimensional incompressible Navier--Stokes equations based on a hybrid discretization of both the velocity and pressure variables. The proposed method is pressure-robust, i.e., irrotational forcing terms do not affect the approximation of the velocity, and Reynolds-quasi-robust, with error estimates that, for smooth enough exact solutions, do not depend on the inverse of the viscosity. We carry out an in-depth convergence analysis highlighting pre-asymptotic convergence rates and validate the theoretical findings with a complete set of numerical experiments.

math.NA↗

arXiv2024

A Péclet-robust discontinuous Galerkin method for nonlinear diffusion with advection

We analyze a Discontinuous Galerkin method for a problem with linear advection-reaction and $p$-type diffusion, with Sobolev indices $p\in (1, \infty)$. The discretization of the diffusion term is based on the full gradient including jump liftings and interior-penalty stabilization while, for the advective contribution, we consider a strengthened version of the classical upwind scheme. The developed error estimates track the dependence of the local contributions to the error on local Péclet numbers. A set of numerical tests supports the theoretical derivations.

math.NA↗