Related papers: Algebraic Hybridization and Static Condensation wi…
We present a domain decomposition formulation based on hybridization which is inspired by hybridized discontinuous Galerkin (HDG) methods, that enhance mixed domain decomposition methods by incorporating stabilization terms. Unlike…
In this work, we develop a fully implicit Hybrid High-Order algorithm for the Cahn-Hilliard problem in mixed form. The space discretization hinges on local reconstruction operators from hybrid polynomial unknowns at elements and faces. The…
Within the finite element community, discontinuous Galerkin (DG) and mixed finite element methods have become increasingly popular in simulating geophysical flows. However, robust and efficient solvers for the resulting saddle-point and…
In this contribution, we extend the hybridization framework for the Hodge Laplacian [Awanou et al., Hybridization and postprocessing in finite element exterior calculus, 2023] to port-Hamiltonian systems describing linear wave propagation…
An algebraic multilevel iteration method for solving system of linear algebraic equations arising in $H(\mathrm{curl})$ and $H(\mathrm{div})$ spaces are presented. The algorithm is developed for the discrete problem obtained by using the…
We present the hybridization of flux reconstruction methods for advection-diffusion problems. Hybridization introduces a new variable into the problem so that it can be reduced via static condensation. This allows the solution of implicit…
In this work we study arbitrary-order hybrid discretizations of Friedrichs systems. Friedrichs systems provide a framework that goes beyond the standard classification of partial differential equations into hyperbolic or elliptic, and are…
Compatible finite element discretisations for the atmospheric equations of motion have recently attracted considerable interest. Semi-implicit timestepping methods require the repeated solution of a large saddle-point system of linear…
This article reports on the confluence of two streams of research, one emanating from the fields of numerical analysis and scientific computation, the other from topology and geometry. In it we consider the numerical discretization of…
We propose a variational splitting technique for the generalized-$\alpha$ method to solve hyperbolic partial differential equations. We use tensor-product meshes to develop the splitting method, which has a computational cost that grows…
We introduce a new preconditioner for a recently developed pressure-robust hybridized discontinuous Galerkin (HDG) finite element discretization of the Stokes equations. A feature of HDG methods is the straightforward elimination of…
We propose a $p$-multilevel preconditioner for Hybrid High-Order discretizations (HHO) of the Stokes equation, numerically assess its performance on two variants of the method, and compare with a classical Discontinuous Galerkin scheme. We…
We develop a hybrid spatial discretization for the wave equation in second order form, based on high-order accurate finite difference methods and discontinuous Galerkin methods. The hybridization combines computational efficiency of finite…
An abstract framework is developed that enables the analysis of algebraically stabilized discretizations in a unified way. This framework is applied to a discretization of this kind for convection-diffusion-reaction equations. The…
This article aims to demonstrate and discuss the applications of automatic differentiation (AD) for finding derivatives in PDE-constrained optimization problems and Jacobians in non-linear finite element analysis. The main idea is to…
Boundary element methods for the Helmholtz equation lead to large dense matrices that can only be handled if efficient compression techniques are used. Directional compression techniques can reach good compression rates even for…
The accurate numerical simulation of turbulent incompressible flows is a challenging topic in computational fluid dynamics. For discretisation methods to be robust in the under-resolved regime, mass conservation as well as energy stability…
We present a comparison between hybridized and non-hybridized discontinuous Galerkin methods in the context of target-based hp-adaptation for compressible flow problems. The aim is to provide a critical assessment of the computational…
Solving the reactive low-Mach Navier-Stokes equations with high-order adaptive methods in time is still a challenging problem, in particular due to the handling of the algebraic variables involved in the mass constraint. We focus on the…
We derive and analyze a broad class of finite element methods for numerically simulating the stationary, low Reynolds number flow of concentrated mixtures of several distinct chemical species in a common thermodynamic phase. The underlying…