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arXiv · 2309.13352

A Hybrid High-Order Method for a Class of Strongly Nonlinear Elliptic Boundary Value Problems

Gouranga Mallik·Thirupathi Gudi
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Abstract

In this article, we design and analyze a Hybrid High-Order (HHO) finite element approximation for a class of strongly nonlinear boundary value problems. We consider an HHO discretization for a suitable linearized problem and show its well-posedness using the Gardings type inequality. The essential ingredients for the HHO approximation involve local reconstruction and high-order stabilization. We establish the existence of a unique solution for the HHO approximation using the Brouwer fixed point theorem and contraction principle. We derive an optimal order a priori error estimate in the discrete energy norm. Numerical experiments are performed to illustrate the convergence histories.

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Gouranga Mallik, Thirupathi Gudi. 2023-09-23. A Hybrid High-Order Method for a Class of Strongly Nonlinear Elliptic Boundary Value Problems. https://arxiv.org/abs/2309.13352

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