Mallik, Gouranga ; Gudi, Thirupathi (2023) A Hybrid High-Order Method for a Class of Strongly Nonlinear Elliptic Boundary Value Problems Journal of Scientific Computing, 98 (1). ISSN 0885-7474
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Official URL: https://doi.org/10.1007/s10915-023-02390-4
Related URL: http://dx.doi.org/10.1007/s10915-023-02390-4
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 Garding 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.
| Item Type: | Article |
|---|---|
| Source: | Copyright of this article belongs to Springer Nature Switzerland AG. |
| Keywords: | Hybrid High-Order Methods; ;Second-Order Nonlinear Elliptic Problems; Brouwer Fixed Point Theorem; .Error Estimates |
| ID Code: | 141606 |
| Deposited On: | 02 Dec 2025 05:36 |
| Last Modified: | 02 Dec 2025 05:36 |
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