Related papers: Adjoint-Based Error Estimation and Mesh Adaptation…
We present improved $L^2$-error estimates on the time-integrated primal variable for the wave equation in its first-order formulation. The space discretization relies on a hybrid nonconforming method, such as the hybridizable discontinuous…
We present a novel high-order accurate nodal discontinuous Galerkin (DG) method for solving nonlinear hyperbolic systems of partial differential equations (PDEs) on fully unstructured three-dimensional polyhedral meshes. A mesh generator is…
We introduce a hybridized discontinuous Galerkin method for the incompressible Reynolds Averaged Navier-Stokes equations coupled with the Spalart-Allmaras one equation turbulence model. With a special choice of velocity and pressure spaces…
This paper investigates the efficiency, robustness, and scalability of approximate ideal restriction (AIR) algebraic multigrid as a preconditioner in the all-at-once solution of a space-time hybridizable discontinuous Galerkin (HDG)…
We use the ideas of goal-oriented error estimation and adaptivity to design and implement an efficient adaptive algorithm for approximating linear quantities of interest derived from solutions to elliptic partial differential equations…
We study the numerical approximation of advection-diffusion equations with highly oscillatory coefficients and possibly dominant advection terms by means of the Multiscale Finite Element Method. The latter method is a now classical, finite…
We propose a multiscale spectral generalized finite element method (MS-GFEM) for discontinuous Galerkin (DG) discretizations. The method builds local approximations on overlapping subdomains as the sum of a local source solution and a…
We combine the newly-constructed Galerkin difference basis with the energy-based discontinuous Galerkin method for wave equations in second order form. The approximation properties of the resulting method are excellent and the allowable…
The dynamic behavior of jointed assemblies exhibiting friction nonlinearities features amplitude-dependent dissipation and stiffness. To develop numerical simulations for predictive and design purposes, macro-scale High Fidelity Models…
We present a new line-based discontinuous Galerkin (DG) discretization scheme for first- and second-order systems of partial differential equations. The scheme is based on fully unstructured meshes of quadrilateral or hexahedral elements,…
We devised a first order time stepping ensemble hybridizable discontinuous Galerkin (HDG) method for a group of parameterized convection diffusion PDEs with different initial conditions, body forces, boundary conditions and coefficients in…
We propose and analyze a hybridizable discontinuous Galerkin (HDG) method for solving a mixed magnetic advection-diffusion problem within a more general Friedrichs system framework. With carefully constructed numerical traces, we introduce…
We investigate the problem of center estimation in the high dimensional binary sub-Gaussian Mixture Model with Hidden Markov structure on the labels. We first study the limitations of existing results in the high dimensional setting and…
We deal with the numerical solution of the time-dependent partial differential equations using the adaptive space-time discontinuous Galerkin (DG) method. The discretization leads to a nonlinear algebraic system at each time level, the size…
We present new aposteriori error estimates for the interior penalty discontinuous Galerkin method applied to non-stationary convection-diffusion equations. The focus is on strongly convection-dominated problems without zeroth-order reaction…
In this work we present an a priori error analysis for solving the unsteady advection equation on cut cell meshes along a straight ramp in two dimensions. The space discretization uses a lowest order upwind-type discontinuous Galerkin…
We study the convergence of the new family of mimetic finite difference schemes for linear diffusion problems recently proposed in [38]. In contrast to the conventional approach, the diffusion coefficient enters both the primary mimetic…
Traditional time-domain discontinuous Galerkin (DG) methods result in large storage costs at high orders of approximation due to the storage of dense elemental matrices. In this work, we propose a weight-adjusted DG (WADG) methods for…
Multi-adaptive Galerkin methods are extensions of the standard continuous and discontinuous Galerkin methods for the numerical solution of initial value problems for ordinary or partial differential equations. In particular, the…
We investigate a numerical behaviour of robust deterministic optimal control problem subject to a convection diffusion equation containing uncertain inputs. Stochastic Galerkin approach, turning the original optimization problem containing…