Veselin Dobrev

TL;DR: This paper presents a general framework for high-order Lagrangian discretization of these compressible shock hydrodynamics equations using curvilinear finite elements for any finite dimensional approximation of the kinematic and thermodynamic fields.

TL;DR: MFEM as mentioned in this paper is an open-source, lightweight, flexible and scalable C++ library for modular finite element methods that features arbitrary high-order finite element meshes and spaces, support for a wide variety of discretization approaches and emphasis on usability, portability, and highperformance computing efficiency.

TL;DR: This paper reviews some known and proposes some new preconditioning methods for a number of discontinuous Galerkin finite element approximations for elliptic problems of second order and presents numerical experiments for 3‐D model problem showing uniform convergence of the constructed methods.

TL;DR: A two-grid convergence theory for the parallel-in-time scheme known as multigrid reduction in time (MGRIT), as it is implemented in the open-source package XBraid, and presents a two-level MGRIT convergence analysis for linear problems where the spatial discretization matrix can be diagonalized.