This article is concerned with the numerical solution of convex variational problems. More precisely, we develop an iterative minimisation technique which allows for the successive enrichment of an underlying discrete approximation space in an adaptive manner. Specifically, we outline a new approach in the context of hp-adaptive finite element methods employed for the efficient numerical solution of linear and nonlinear second-order boundary value problems. Numerical experiments are presented which highlight the practical performance of this new hp-refinement technique for both one- and two-dimensional problems.
Houston, P., & Wihler, T. P. (2016). Adaptive energy minimisation for hp-finite element methods. Computers and Mathematics with Applications, 71(4), https://doi.org/10.1016/j.camwa.2016.01.002