Advances in Applied Mechanics, Volume 63 highlights new advances, with this volume presenting interesting chapters written by an international board of authors. Chapters in this release cover higher order discontinuous Galerkin finite element methods for the contact problems, Anisotropic Recovery-Based Error Estimators and Mesh Adaptation Tailored for Real-Life Engineering Innovation, Adaptive mesh refinement on Cartesian meshes applied to the mixed finite element discretization of the multigroup neutron diffusion equations, and more. Other sections cover a posteriori error analysis for Finite Element approximation of some groundwater models Part I: Linear models, a posteriori error estimates for low frequency electromagnetic computations, and more.