M. Djaghout, A. Chaoui, K. Zennir, “On the discretization of evolution <nobr>$p$</nobr>-bi-Laplace equation”, Sib. Zh. Vychisl. Mat., 2022, Volume 25, Number 4,Pages <nobr>371

This article is cited in 5 papers

On the discretization of evolution $p$-bi-Laplace equation

M. Djaghout^a, A. Chaoui^a, K. Zennir^b

^a Laboratoire de Mathématiques Appliquées et de Modélisation, Faculté de Mathématiques et de l’Informatique et des Sciences de la Matiére, Université 8 Mai 1945 Guelma, B.P. 401, 24000, Guelma, Algérie
^b Department of Mathematics, College of Sciences and Arts, Qassim University, Ar-Rass, Saudi Arabia

Abstract: This article discusses the mixed finite element method combined with backward-Euler method to study the hyperbolic $p$-bi-Laplace equation, where the existence and uniqueness of solution for discretized problem is shown in Lebesgue Sobolev spaces. The mixed formulation and the inf–sup condition are then given to prove the well posed of the scheme and the optimal a priori error estimates for fully discrete schemes is extracted. Finally, a numerical example is given to confirm the theoretical results obtained.

Key words: evolution $p$-bi-Laplace equation, mixed finite element method, inf–sup condition and mixed formulation, existence and uniqueness.

MSC: 35G30, 35G05, 65N30

Received: 09.12.2021
Revised: 15.04.2022
Accepted: 18.07.2022

DOI: 10.15372/SJNM20220403