相关论文: Numerical solution of steady-state groundwater flo…

We propose an embedded discontinuous Galerkin (EDG) method to approximate the solution of a distributed control problem governed by convection diffusion PDEs, and obtain optimal a priori error estimates for the state, dual state, their…

We investigate the numerical performance of a Discontinuous Galerkin (DG) hydrodynamics implementation when applied to the problem of driven, isothermal supersonic turbulence. While the high-order element-based spectral approach of DG is…

Discontinuous Galerkin (DG) methods are known to suffer from increasingly restrictive explicit time-step constraints as the polynomial order increases, limiting their efficiency at high orders for explicit time-stepping schemes. In this…

We study the numerical approximation of singularly perturbed convection-diffusion problems on one-dimensional pipe networks. In the vanishing diffusion limit, the number and type of boundary conditions and coupling conditions at network…

Discontinuous Galerkin (DG) methods are promising high order discretizations for unsteady compressible flows. Here, we focus on Numerical Weather Prediction (NWP). These flows are characterized by a fine resolution in $z$-direction and low…

High-order Discontinuous Galerkin Spectral Element Methods (DGSEM) provide excellent accuracy for complex flow simulations, but their computational cost increases sharply with higher polynomial orders. %that provide very accurate solutions.…

We discuss the mathematical modeling and numerical discretization of transport problems on one-dimensional networks. Suitable coupling conditions are derived that guarantee conservation of mass across network junctions and dissipation of a…

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…

Kinetic schemes for compressible flow of gases are constructed by exploiting the connection between Boltzmann equation and the Navier-Stokes equations. This connection allows us to construct a flux splitting for the Navier-Stokes equations…

In this work, using a unified framework consisting of third-order accurate discontinuous Galerkin schemes, we perform a comparison between five different numerical approaches to the free-surface shallow flow simulation on bottom steps.…

Heterogeneous computing and exploiting integrated CPU-GPU architectures has become a clear current trend since the flattening of Moore's Law. In this work, we propose a numerical and algorithmic re-design of a p-adaptive quadrature-free…

We propose and analyze an iterative high-order hybridized discontinuous Galerkin (iHDG) discretization for linear partial differential equations. We improve our previous work (SIAM J. Sci. Comput. Vol. 39, No. 5, pp. S782--S808) in several…

The tempered fractional diffusion equation could be recognized as the generalization of the classic fractional diffusion equation that the truncation effects are included in the bounded domains. This paper focuses on designing the high…

We consider time discretization methods for abstract parabolic problems with inhomogeneous linear constraints. Prototype examples that fit into the general framework are the heat equation with inhomogeneous (time dependent) Dirichlet…

The accurate numerical simulation of high Reynolds number incompressible flows is a challenging topic in computational fluid dynamics. Classical inf-sup stable methods like the Taylor-Hood element or only $L^2$-conforming discontinuous…

A numerical method based on the hybridizable discontinuous Galerkin method in space and backward Euler in time is formulated and analyzed for solving the miscible displacement problem. Under low regularity assumptions, convergence is…

This paper investigates the supercloseness of a singularly perturbed convection diffusion problem using the direct discontinuous Galerkin (DDG) method on a Shishkin mesh. The main technical difficulties lie in controlling the diffusion term…

We present a numerical approximation of Darcy's flow through a porous medium that incorporates networks of fractures with non empty intersection. Our scheme employs PolyDG methods, i.e. discontinuous Galerkin methods on general polygonal…

We devise a stabilized method to weakly enforce bound constraints in the discrete solution of advection-dominated diffusion problems. This method combines a nonlinear penalty formulation with a discontinuous Galerkin-based residual…

In this paper, we develop a Discontinuous Galerkin (DG) method for solving H(curl)-elliptic hemivariational inequalities. By selecting an appropriate numerical flux, we construct an Interior Penalty Discontinuous Galerkin (IPDG) scheme. A…