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A Hybrid-High Order Method for Quasilinear Elliptic Problems of Nonmonotone Type

Gudi, T and Mallik, G and Pramanick, T (2022) A Hybrid-High Order Method for Quasilinear Elliptic Problems of Nonmonotone Type. In: SIAM Journal on Numerical Analysis, 60 (4). pp. 2318-2344.

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Official URL: https://doi.org/10.1137/21M1412050


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.

Item Type: Journal Article
Publication: SIAM Journal on Numerical Analysis
Publisher: Society for Industrial and Applied Mathematics Publications
Additional Information: The copyright for this article belongs to Society for Industrial and Applied Mathematics Publications.
Keywords: Computational mechanics; Functional analysis; Topology, Brouwer fixed point theorem; Design and analysis; Error estimates; High-order methods; Higher-order methods; Hybrid high-order method; Nonmonotone; Quasi-linear elliptic problems; Second orders; Second-order quasilinear elliptic problem, Fixed point arithmetic
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 04 Jan 2023 05:51
Last Modified: 04 Jan 2023 05:51
URI: https://eprints.iisc.ac.in/id/eprint/78707

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