English
Related papers

Related papers: Polytopal discontinuous Galerkin discretization of…

200 papers

We study higher-order space-time variational discretisations for modeling complex processes in porous media that include fluid and structure interactions which are of fundamental importance in many engineering fields with applications in…

Numerical Analysis · Mathematics 2018-05-03 Uwe Köcher , Markus Bause

In this work, we present an iteratively decoupled algorithm for solving the quasi-static multiple-network poroelastic model. Our approach employs a total-pressure-based formulation with solid displacement, total pressure, and network…

Numerical Analysis · Mathematics 2025-07-21 Mingchao Cai , Meng Lei , Jingzhi Li , Jiaao Sun , Feng Wang

In this paper we formulate and test numerically a fully-coupled discontinuous Galerkin (DG) method for incompressible two-phase flow with discontinuous capillary pressure. The spatial discretization uses the symmetric interior penalty DG…

Fluid Dynamics · Physics 2013-10-01 Peter Bastian

Unstructured grid ocean models are advantageous for simulating the coastal ocean and river-estuary-plume systems. However, unstructured grid models tend to be diffusive and/or computationally expensive which limits their applicability to…

Atmospheric and Oceanic Physics · Physics 2018-10-31 Tuomas Kärnä , Stephan C. Kramer , Lawrence Mitchell , David A. Ham , Matthew D. Piggott , António M. Baptista

This paper develops and analyses semi-discrete numerical method for two dimensional Vlasov-Stokes' system with periodic boundary condition. The method is based on coupling of semi-discrete discontinuous Galerkin method for the Vlasov…

Numerical Analysis · Mathematics 2023-12-18 Harsha Hutridurga , Krishan Kumar , Amiya K. Pani

We introduce a general framework for approximating parabolic Stochastic Partial Differential Equations (SPDEs) based on fluctuation-dissipation balance. Using this approach we formulate Stochastic Discontinuous Galerkin Methods (SDGM). We…

Numerical Analysis · Mathematics 2023-02-28 Will Pazner , Nathaniel Trask , Paul J. Atzberger

The aim of this work is to introduce and analyze a finite element discontinuous Galerkin method on polygonal meshes for the numerical discretization of acoustic waves propagation through poroelastic materials. Wave propagation is modeled by…

Numerical Analysis · Mathematics 2021-04-14 Paola F. Antonietti , Michele Botti , Ilario Mazzieri , Simone Nati Poltri

We present and analyze a discontinuous Galerkin method for the numerical modelling of the non-linear fully-coupled thermo-poroelastic problem. For the spatial discretization, we design a high-order discontinuous Galerkin method on polygonal…

Numerical Analysis · Mathematics 2022-05-27 Paola F. Antonietti , Stefano Bonetti , Michele Botti

This article investigates matrix-free higher-order discontinuous Galerkin discretizations of the Navier--Stokes equations for incompressible flows with variable viscosity. The viscosity field may be prescribed analytically or governed by a…

Computational Engineering, Finance, and Science · Computer Science 2025-11-04 Richard Schussnig , Niklas Fehn , Douglas Ramalho Queiroz Pacheco , Martin Kronbichler

Gaseous flows show a diverse set of behaviors on different characteristic scales. Given the coarse-grained modeling in theories of fluids, considerable uncertainties may exist between the flow-field solutions and the real physics. To study…

Computational Physics · Physics 2021-05-05 Tianbai Xiao , Martin Frank

One- and multi-dimensional stochastic Maxwell equations with additive noise are considered in this paper. It is known that such system can be written in the multi-symplectic structure, and the stochastic energy increases linearly in time.…

Numerical Analysis · Mathematics 2022-05-04 Jiawei Sun , Chi-Wang Shu , Yulong Xing

This work focuses on the development of efficient solvers for the pseudo-stress formulation of the unsteady Stokes problem, discretised by means of a discontinuous Galerkin method on polytopal grids (PolyDG). The introduction of the…

Numerical Analysis · Mathematics 2026-02-04 Paola F. Antonietti , Alessandra Cancrini , Gabriele Ciaramella

Multiscale mathematical models have shown great promise in computational brain electrophysiology but are still hindered by high computational costs due to fast dynamics and complex brain geometries, requiring very fine spatio-temporal…

Numerical Analysis · Mathematics 2025-05-01 Caterina Beatrice Leimer Saglio , Stefano Pagani , Paola F. Antonietti

In this work we review discontinuous Galerkin finite element methods on polytopal grids (PolydG) for the numerical simulation of multiphysics wave propagation phenomena in heterogeneous media. In particular, we address wave phenomena in…

Numerical Analysis · Mathematics 2021-11-04 Paola F. Antonietti , Michele Botti , Ilario Mazzieri

Divergence-free discontinuous Galerkin (DG) finite element methods offer a suitable discretization for the pointwise divergence-free numerical solution of Borrvall and Petersson's model for the topology optimization of fluids in Stokes flow…

Numerical Analysis · Mathematics 2022-02-22 Ioannis P. A. Papadopoulos

We present an efficient nodal discontinuous Galerkin method for approximating nearly incompressible flows using the Boltzmann equations. The equations are discretized with Hermite polynomials in velocity space yielding a first order…

Numerical Analysis · Mathematics 2019-05-22 A. Karakus , N. Chalmers , J. S. Hesthaven , T. Warburton

In this work, we introduce a time memory formalism in poroelasticity model that couples the pressure and displacement. We assume this multiphysics process occurs in multicontinuum media. The mathematical model contains a coupled system of…

Numerical Analysis · Mathematics 2022-01-20 Aleksei Tyrylgin , Maria Vasilyeva , Anatoly Alikhanov , Dongwoo Sheen

We present a high-order space-time discretization equipped with fully-discrete entropy stability properties for general choices of volume and surface quadrature rules. The formulation uses flux reconstruction (FR) in the spatial dimension…

Numerical Analysis · Mathematics 2026-04-23 Carolyn M. V. Pethrick , Siva Nadarajah

The Stokes equations play an important role in the incompressible flow simulation. In this paper, a novel divergence-free parametric mixed finite element method is proposed for solving three-dimensional Stokes equations on domains with…

Numerical Analysis · Mathematics 2025-12-19 Lingxiao Li , Haiyan Su , He Zhang , Weiying Zheng

In (J. Comput. Phys., 417, 109577, 2020) we introduced a space-time embedded-hybridizable discontinuous Galerkin method for the solution of the incompressible Navier-Stokes equations on time-dependent domains of which the motion of the…

Numerical Analysis · Mathematics 2023-07-07 Tamas L. Horvath , S. Rhebergen