In this paper we will review a recent emerging paradigm shift in the construction and
analysis of high order Discontinuous Galerkin methods applied to approximate solutions of …

The aim of the present chapter is to provide an in‐depth survey of arbitrary Lagrangian–
Eulerian (ALE) methods, including both conceptual aspects of the mixed kinematical …

Theoretical studies and numerical experiments suggest that unstructured high-order
methods can provide solutions to otherwise intractable fluid flow problems within complex …

We propose a general---ie, independent of the underlying equation---registration method for
parameterized model order reduction. Given the spatial domain Ω⊂R^d and the manifold …

We present hybridizable discontinuous Galerkin methods for solving steady and time-
dependent partial differential equations (PDEs) in continuum mechanics. The essential …

This work introduces a new approach to reduce the computational cost of solving partial
differential equations (PDEs) with convection-dominated solutions: model reduction with …

The flux reconstruction (FR) approach unifies various high-order schemes, including
collocation based nodal discontinuous Galerkin methods, and all spectral difference …

A moving discontinuous Galerkin finite element method with interface condition enforcement
is formulated for flows with discontinuous interfaces. The underlying weak formulation …

This work introduces a novel discontinuity-tracking framework for resolving discontinuous
solutions of conservation laws with high-order numerical discretizations that support inter …

We present an approach for constructing finite-volume methods for flux-divergence forms to
any order of accuracy defined as the image of a smooth mapping from a rectangular …