2023/09/23 by Mallik, Gouranga, Gudi, Thirupathi · 1 citation
#FOS: Mathematics #Numerical Analysis (math.NA)
paper · doi:10.48550/arxiv.2309.13352
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.