Computational Calculus of Variations

The finite element method (FEM) is one of the most widely used approaches for solving variational problems. In this talk, we will provide a brief introduction to FEM before exploring key analytical techniques used to study these methods. A central theme of the presentation is the deep interplay between numerical schemes and analytical insights. Our focus will be on the p-Laplace operator and convex energy functionals exhibiting non-standard growth conditions, particularly those affected by the Lavrentiev gap phenomenon. This discussion will shed light on the challenges and nuances in the (numerical) analysis of such variational problems.