In recent years, high-order discontinuous Galerkin (DG) methods have emerged as an
attractive approach for numerical simulations of compressible flows. This paper presents an …

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 …

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

A novel framework for resolving discontinuous solutions of conservation laws, eg, contact
lines, shock waves, and interfaces, using implicit tracking and a high-order discontinuous …

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

In this paper, we develop high-order nodal discontinuous Galerkin (DG) methods for
hyperbolic conservation laws that satisfy invariant domain preserving properties using …

We propose a model reduction procedure for rapid and reliable solution of parameterized
hyperbolic partial differential equations. Due to the presence of parameter-dependent shock …

High-order implicit shock tracking (fitting) is a class of high-order, optimization-based
numerical methods to approximate solutions of conservation laws with non-smooth features …

High-order implicit shock tracking (fitting) is a new class of numerical methods to
approximate solutions of conservation laws with non-smooth features, eg, contact lines …

The moving discontinuous Galerkin finite element method with interface condition
enforcement is applied to the case of viscous flows. This method uses a weak formulation …