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The paper proposes a new, conservative fully-discrete scheme for the numerical solution of the regularised shallow water Boussinesq system of equations in the cases of periodic and reflective boundary conditions. The particular system is…

Numerical Analysis · Mathematics 2021-05-12 Dimitrios Mitsotakis , Hendrik Ranocha , David I. Ketcheson , Endre Süli

Multilayered poroelastic structures are found in many biological tissues such as cartilage and the cornea, and play a key role in the design of bioartificial organs and other bioengineering applications. Motivated by these applications, we…

Numerical Analysis · Mathematics 2025-07-15 Andrew Scharf , Martina Bukač , Sunčica Čanić

We present and analyze a discontinuous Galerkin method for the numerical modeling of a Kelvin-Voigt thermo/poro-viscoelastic problem. We present the derivation of the model and we develop a stability analysis in the continuous setting that…

Numerical Analysis · Mathematics 2025-08-01 Stefano Bonetti , Mattia Corti

In this article we study the numerical approximation of incompressible miscible displacement problems with a linearised Crank-Nicolson time discretisation, combined with a mixed finite element and discontinuous Galerkin method. At the heart…

Numerical Analysis · Mathematics 2011-11-28 Max Jensen , Ruediger Mueller

We present a GPU-accelerated version of a high-order discontinuous Galerkin discretization of the unsteady incompressible Navier-Stokes equations. The equations are discretized in time using a semi-implicit scheme with explicit treatment of…

Numerical Analysis · Mathematics 2018-05-08 Ali Karakus , Noel Chalmers , Kasia Swirydowicz , Timothy Warburton

In this article we obtain an optimal best approximation type result for fully discrete approximations of the transient Stokes problem. For the time discretization we use the discontinuous Galerkin method and for the spatial discretization…

Numerical Analysis · Mathematics 2021-07-26 Niklas Behringer , Dmitriy Leykekhman , Boris Vexler

In this paper, we propose an accurate numerical means built upon a spectral-Galerkin method in spatial discretization and an enriched multi-step spectral-collocation approach in temporal direction, for Maxwell equations in Cole-Cole…

Numerical Analysis · Mathematics 2018-01-25 Can Huang , Li-lian Wang

High-order accurate discontinuous Galerkin (DG) methods have emerged as powerful tools for solving partial differential equations such as the compressible Navier-Stokes equations due to their excellent dispersion-dissipation properties and…

Numerical Analysis · Mathematics 2025-11-12 Patrick Kopper , Anna Schwarz , Jens Keim , Andrea Beck

We propose and rigorously analyse semi- and fully discrete discontinuous Galerkin methods for an initial and boundary value problem describing inertial viscoelasticity in terms of elastic and viscoelastic stress components, and with mixed…

Numerical Analysis · Mathematics 2023-06-27 Salim Meddahi , Ricardo Ruiz-Baier

The modeling of complicated time-evolving physical dynamics from partial observations is a long-standing challenge. Particularly, observations can be sparsely distributed in a seemingly random or unstructured manner, making it difficult to…

Computer Vision and Pattern Recognition · Computer Science 2025-10-23 Fan Xu , Hao Wu , Nan Wang , Lilan Peng , Kun Wang , Wei Gong , Xibin Zhao

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,…

Numerical Analysis · Mathematics 2015-06-04 Per-Olof Persson

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,…

Numerical Analysis · Mathematics 2021-01-25 Andrea Barth , Andreas Stein

The shallow water equations (SWE) are a commonly used model to study tsunamis, tides, and coastal ocean circulation. However, there exist various approaches to discretize and solve them efficiently. Which of them is best for a certain…

Mathematical Software · Computer Science 2019-04-19 Sara Faghih-Naini , Sebastian Kuckuk , Vadym Aizinger , Daniel Zint , Roberto Grosso , Harald Köstler

In this article, we propose a Milstein finite difference scheme for a stochastic partial differential equation (SPDE) describing a large particle system. We show, by means of Fourier analysis, that the discretisation on an unbounded domain…

Numerical Analysis · Mathematics 2012-04-09 Michael B. Giles , Christoph Reisinger

We present and analyze in a unified setting two schemes for the numerical discretization of a Darcy-Forchheimer fluid flow model coupled with an advection-diffusion equation modeling the temperature distribution in the fluid. The first…

Numerical Analysis · Mathematics 2026-02-11 Stefano Bonetti , Michele Botti , Paola F. Antonietti

A local weighted discontinuous Galerkin gradient discretization method for solving elliptic equations is introduced. The local scheme is based on a coarse grid and successively improves the solution solving a sequence of local elliptic…

Numerical Analysis · Mathematics 2018-07-30 Assyr Abdulle , Giacomo Rosilho de Souza

Mathematical modeling at the level of the full cardiovascular system requires the numerical approximation of solutions to a one-dimensional nonlinear hyperbolic system describing flow in a single vessel. This model is often simulated by…

Computational Physics · Physics 2015-04-22 Sebastian Acosta , Charles Puelz , Beatrice Riviere , Daniel J. Penny , Craig G. Rusin

In this paper we propose a new spatially high order accurate semi-implicit discontinuous Galerkin (DG) method for the solution of the two dimensional incompressible Navier-Stokes equations on staggered unstructured curved meshes. While the…

Numerical Analysis · Mathematics 2014-07-07 Maurizio Tavelli , Michael Dumbser

The article describes parallel multiphysics simulations of charged particles in microfluidic flows with the waLBerla framework. To this end, three physical effects are coupled: rigid body dynamics, fluid flow modelled by a lattice Boltzmann…

Computational Engineering, Finance, and Science · Computer Science 2014-10-27 Dominik Bartuschat , Ulrich Rüde

We introduce and analyze a hybridizable discontinuous Galerkin (HDG) method for the dual-porosity-Stokes problem. This coupled problem describes the interaction between free flow in macrofractures/conduits, governed by the Stokes equations,…

Numerical Analysis · Mathematics 2023-08-30 Aycil Cesmelioglu , Jeonghun J. Lee , Sander Rhebergen , Dorisa Tabaku