Galerkin Approximation: Irreducible and Mixed Forms

This chapter covers Galerkin approximations: irreducible and mixed formulations. It introduces the use of weak formulations to construct finite element-based approximate solutions, leading to the well-known Galerkin method. Assuming that readers may not be familiar with the finite element method for small deformation linear problems, the chapter provides a complete overview of the fundamental steps for solving transient problems and the solution of nonlinear algebraic systems, considering both irreducible and mixed approximation approaches. The chapter concludes with a thermal analysis example based on nonlinear quasi-harmonic equations.