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arXiv · 2510.15574

A Hybrid High-Order Finite Element Method for a Nonlocal Nonlinear Problem of Kirchhoff Type

Gouranga Mallik
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Abstract

In this article, we design and analyze a hybrid high-order (HHO) finite element approximation for the solution of a nonlocal nonlinear problem of Kirchhoff type. The HHO method involves arbitrary-order polynomial approximations on structured and unstructured polytopal meshes. We establish the existence of a unique discrete solution to the nonlocal nonlinear discrete problem. We derive an optimal-order error estimate in the discrete energy norm. The discrete system is solved using Newton's iterations on the sparse matrix system. We perform numerical tests to substantiate the theoretical results.

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Gouranga Mallik. 2025-10-17. A Hybrid High-Order Finite Element Method for a Nonlocal Nonlinear Problem of Kirchhoff Type. https://arxiv.org/abs/2510.15574

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