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arXiv · 2606.07477

A Mixed Virtual Element Method for the p-Laplace equation

Kirubell B. Haile·Giuseppe Vacca
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Abstract

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.

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Kirubell B. Haile, Giuseppe Vacca. 2026-06-05. A Mixed Virtual Element Method for the p-Laplace equation. https://arxiv.org/abs/2606.07477

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