M. Dehimi, A. Chaoui

Galerkin Method Applied to $p(\cdot)$-Bi-Laplace Equation with Variable Exponent

abstract:
In this article, a Galerkin mixed finite element method is proposed to find the numerical solutions of high order $p(\cdot)$-bi-Laplace equations. The well-posedness of the problem in suitable Lebesgue-Sobolev spaces with variable exponent owing to nonlinear monotone operator theory is investigated. Some a priori error estimates are shown by using the Galerkin orthogonality properties and variable exponent Lebesgue-Sobolev continues embedding.

Mathematics Subject Classification: 35G30, 35G05, 65N30

Key words and phrases: $p(\cdot)$-bi-Laplace equation, Galerkin method, weak solution, error estimate