Related papers: Postprocessing of Non-Conservative Flux for Compat…
Numerical simulation of flow problems and wave propagation in heterogeneous media has important applications in many engineering areas. However, numerical solutions on the fine grid are often prohibitively expensive, and multiscale model…
We propose a new Neural Galerkin Normalizing Flow framework to approximate the transition probability density function of a diffusion process by solving the corresponding Fokker-Planck equation with an atomic initial distribution,…
For finite element approximations of transport phenomena, it is often necessary to apply a form of limiting to ensure that the discrete solution remains well-behaved and satisfies physical constraints. However, these limiting procedures are…
We present a robust and accurate discretization approach for incompressible turbulent flows based on high-order discontinuous Galerkin methods. The DG discretization of the incompressible Navier-Stokes equations uses the local…
In this article, we present an Unfitted Space-Time Finite Element method for the scalar transport equation posed on moving domains. We consider the case of the domain boundary being transported by the same velocity field as the scalar…
We consider the discretization of a semilinear damped wave equation arising, for instance, in the modeling of gas transport in pipeline networks. For time invariant boundary data, the solutions of the problem are shown to converge…
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…
The work is devoted to the development and computational implementation of the homogenization method for modeling unsteady flows of a viscous incompressible fluid in periodic porous media taking into account memory effects. At the…
This paper investigates density driven flow in porous media, focusing on the roles of viscosity contrast, density contrast, and linear adsorption. In this setup, the fluid on top is heavier and more viscous than the fluid below. Under the…
We present a new method for simulating incompressible immiscible two-phase flow in porous media. The semi-implicit method decouples the wetting phase pressure and saturation equations. The equations are discretized using a hybridizable…
Grad-div stabilization is a classical remedy in conforming mixed finite element methods for incompressible flow problems, for mitigating velocity errors that are sometimes called poor mass conservation. Such errors arise due to the…
We consider the generalized Forchheimer flows for slightly compressible fluids. Using Muskat's and Ward's general form of Forchheimer equations, we describe the fluid dynamics by a nonlinear degenerate parabolic equation for the density. We…
This work examines the distributed optimal control of generalized Oseen equations with non-constant viscosity. We propose and analyze a new conforming augmented mixed finite element method and a Discontinuous Galerkin (DG) method for the…
In this paper, we describe a stable finite element formulation for advection-diffusion-reaction problems that allows for robust automatic adaptive strategies to be easily implemented. We consider locally vanishing, heterogeneous, and…
Near-optimal computational complexity of an adaptive stochastic Galerkin method with independently refined spatial meshes for elliptic partial differential equations is shown. The method takes advantage of multilevel structure in expansions…
In this paper, we present optimal error estimates of the local discontinuous Galerkin method with generalized numerical fluxes for one-dimensional nonlinear convection-diffusion systems. The upwind-biased flux with adjustable numerical…
In this paper, we investigate the combination of a linear continuous interior penalty type and a non-linear artificial diffusion stabilisation applied to the transport problem, based on continuous Galerkin finite elements in space. This…
An energy-based discontinuous Galerkin method for the advective wave equation is proposed and analyzed. Energy-conserving or energy-dissipating methods follow from simple, mesh-independent choices of the inter-element fluxes, and both…
We introduce the Equilibrated Averaging Residual Method (EARM), a unified equilibrated flux-recovery framework for elliptic interface problems that applies to a broad class of finite element discretizations. The method is applicable in both…
We present a stability and error analysis of an embedded-hybridized discontinuous Galerkin (EDG-HDG) finite element method for coupled Stokes--Darcy flow and transport. The flow problem, governed by the Stokes--Darcy equations, is…