A Hybrid High-Order Method for Quasilinear Elliptic Problems of Nonmonotone Type
Abstract
In this paper, we design and analyze a hybrid high-order approximation for a class of quasilinear elliptic problems of nonmonotone type. The proposed method has several advantages; for instance, it supports an arbitrary order of approximation and general polytopal meshes. The key ingredients involve local reconstruction and high-order stabilization terms. The existence of a unique discrete solution is shown by using Brouwer's fixed point theorem and the contraction principle. A priori error estimation is derived in a discrete energy norm that shows optimal order of convergence. Numerical experiments are performed to substantiate the theoretical results.
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Submitted: 14 April 2021
Accepted: 6 June 2022
Published online: 30 August 2022
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Department of Science and Technology, Ministry of Science and Technology https://doi.org/10.13039/501100001409 : MATRICS, R(IA)/CVR- PDF/2020
National Board for Higher Mathematics https://doi.org/10.13039/501100005276 : 0204/58/2018/R&D-II/14746
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