Related papers: h-multigrid agglomeration based solution strategie…
We present parameter-robust preconditioners for linear systems that arise after applying static condensation to a hybridizable discontinuous Galerkin (HDG) discretization of the time-dependent Stokes problem. Building upon the theoretical…
This work presents a non-linear extension of the high-order discretisation framework based on the Variational Multiscale (VMS) method previously introduced for steady linear problems. We build on the concept of an optimal projector defined…
We discuss the development, verification, and performance of a GPU accelerated discontinuous Galerkin method for the solutions of two dimensional nonlinear shallow water equations. The shallow water equations are hyperbolic partial…
We propose a family of high-order local discontinuous Galerkin (LDG) methods, built on a parametric representation and coupled with a semi-implicit backward Euler time discretization, for isotropic and anisotropic curve-shortening flows.…
In this paper, an error analysis of a three steps two level Galekin finite element method for the two dimensional transient Navier-Stokes equations is discussed. First of all, the problem is discretized in spatial direction by employing…
In this paper we present a numerical approach to solve the Navier-Stokes equations on moving domains with second-order accuracy. The space discretization is based on the ghost-point method, which falls under the category of unfitted…
In this paper, we present a staggered discontinuous Galerkin (SDG) method for a class of nonlinear elliptic equations in two dimensions. The SDG methods have some distinctive advantages, and have been successfully applied to a wide range of…
We propose a high order discontinuous Galerkin (DG) method for solving nonlinear Fokker-Planck equations with a gradient flow structure. For some of these models it is known that the transient solutions converge to steady-states when time…
Standard gradient-based iteration algorithms for optimization, such as gradient descent and its various proximal-based extensions to nonsmooth problems, are known to converge slowly for ill-conditioned problems, sometimes requiring many…
Subsurface flows are commonly modeled by advection-diffusion equations. Insufficient measurements or uncertain material procurement may be accounted for by random coefficients. To represent, for example, transitions in heterogeneous media,…
In the spirit of making high-order discontinuous Galerkin (DG) methods more competitive, researchers have developed the hybridized DG methods, a class of discontinuous Galerkin methods that generalizes the Hybridizable DG (HDG), the…
We present a fast spectral Galerkin scheme for the discretization of boundary integral equations arising from two-dimensional Helmholtz transmission problems in multi-layered periodic structures or gratings. Employing suitably parametrized…
In this paper we present a Local Fourier Analysis of a space-time multigrid solver for a hyperbolic test problem. The space-time discretization is based on arbitrarily high order discontinuous Galerkin spectral element methods in time and a…
In this work we consider a discontinuous Galerkin method for the discretization of the Stokes problem. We use $H(\textrm{div})$-conforming finite elements as they provide major benefits such as exact mass conservation and…
We present a compatible space-time hybridizable/embedded discontinuous Galerkin discretization for nonlinear free-surface waves. We pose this problem in a two-fluid (liquid and gas) domain and use a time-dependent level-set function to…
In this paper, we use an implicit two-derivative deferred correction time discretization approach and combine it with a spatial discretization of the discontinuous Galerkin spectral element method to solve (non-)linear PDEs. The resulting…
Numerical solution of discrete PDEs corresponding to saddle point problems is highly relevant to physical systems such as Stokes flow. However, scaling up numerical solvers for such systems is often met with challenges in efficiency and…
We present a novel spatial discretization for the Cahn-Hilliard equation including transport. The method is given by a mixed discretization for the two elliptic operators, with the phase field and chemical potential discretized in…
This work proposes a superconvergent hybridizable discontinuous Galerkin (HDG) method for the approximation of the Cauchy formulation of the Stokes equation using same degree of polynomials for the primal and mixed variables. The novel…
We present a novel approach to perform agglomeration of polygonal and polyhedral grids based on spatial indices. Agglomeration strategies are a key ingredient in polytopal methods for PDEs as they are used to generate (hierarchies of)…