Mixed finite element method for a beam equation with the p(x)-biharmonic operator.

In this paper, we consider a nonlinear beam equation with the p (x) -biharmonic operator, where the exponent p (x) is a given function. We transform the problem into a system of two differential equations and prove the existence, uniqueness and regularity of the weak solution. Then we formulate the discrete problem associated with that system using the finite element method and prove the existence, uniqueness and stability of the discrete solution. We also investigate the order of convergence and prove some error estimates. Next, we apply the Lagrange basis to obtain an algebraic system of equations. Finally, we implement the computational codes in Matlab software considering the one and two dimensional cases and we present examples to illustrate the theory. • Study of a nonlinear beam equation with the p (x) -biharmonic operator. • Proof of the existence, uniqueness and regularity of the weak solution. • Discrete formulation with the mixed finite element method. • Demonstration of the existence, uniqueness and regularity of the discrete solution. • Numerical simulations with Matlab software for the one and two dimensional cases. [ABSTRACT FROM AUTHOR]