相关论文: A discontinuous Galerkin method on kinetic flockin…
Deterministic solutions of the Boltzmann equation represent a real challenge due to the enormous computational effort which is required to produce such simulations and often stochastic methods such as Direct Simulation Monte Carlo (DSMC)…
A well-balanced moving mesh discontinuous Galerkin (DG) method is proposed for the numerical solution of the Ripa model -- a generalization of the shallow water equations that accounts for effects of water temperature variations.…
In this paper, a fully implicit Crank-Nicolson discontinuous Galerkin method is proposed for solving the Ginzburg-Landau equation. By leveraging a novel analytical technique, we rigorously establish the unique solvability of the constructed…
In this paper, we present a shock capturing discontinuous Galerkin (SC-DG) method for nonlinear systems of conservation laws in several space dimensions and analyze its stability and convergence. The scheme is realized as a space-time…
A conservative discontinuous Galerkin scheme for a nonlinear Dougherty collision operator in full-f long-wavelength gyrokinetics is presented. Analytically this model operator has the advective-diffusive form of Fokker-Planck operators, it…
A new discontinuous Galerkin finite element method for the Stokes equations is developed in the primary velocity-pressure formulation. This method employs discontinuous polynomials for both velocity and pressure on general…
We derive a sufficient condition for asymptotic flocking in the Cucker-Smale model with self-delay (also called reaction delay) and with non-symmetric interaction weights. The condition prescribes smallness of the delay length relative to…
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.…
This paper deals with the Toner-Tu (TT) model, which is a hydrodynamic model describing the collective motion of numerous self-propelled agents. We analytically study the global-in-time well-posedness of the TT model near the steady-state…
We introduce a discontinuous Galerkin method for the mixed formulation of the elasticity eigenproblem with reduced symmetry. The analysis of the resulting discrete eigenproblem does not fit in the standard spectral approximation framework…
In this paper we present energy-conserving, mixed discontinuous Galerkin (DG) and continuous Galerkin (CG) schemes for the solution of a broad class of physical systems described by Hamiltonian evolution equations. These systems often arise…
The property that the velocity $\boldsymbol{u}$ belongs to $L^\infty(0,T;L^2(\Omega)^d)$ is an essential requirement in the definition of energy solutions of models for incompressible fluids. It is, therefore, highly desirable that the…
A novel approach for the stabilization of the Discontinuous Galerkin method based on the Dafermos entropy rate crition is presented. First, estimates for the maximal possible entropy dissipation rate of a weak solution are derived. Second,…
An energy conservative discontinuous Galerkin scheme for a generalised third order KdV type equation is designed. Based on the conservation principle, we propose techniques that allow for the derivation of optimal a priori bounds for the…
Lin, Chan (High order entropy stable discontinuous Galerkin spectral element methods through subcell limiting, 2024) enforces a cell entropy inequality for nodal discontinuous Galerkin methods by combining flux corrected transport…
A non-negativity-preserving cut-cell discontinuous Galerkin method for the degenerate parabolic diffusive wave approximation of the shallow water equation is presented. The method can handle continuous and discontinuous bathymmetry as well…
For the discrete Cucker-Smale's flocking model with a singular communication weight $\psi(s) = s^{-\alpha}$, with $0<\alpha<1/2$ , we prove that the velocity component of certain type of weak solutions is absolutly continuous. This result…
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…
In this work, we present an asymptotic-preserving semi-Lagrangian discontinuous Galerkin scheme for the Boltzmann equation that effectively handles multi-scale transport phenomena. The main challenge lies in designing appropriate moments…
A newly developed weak Galerkin method is proposed to solve parabolic equations. This method allows the usage of totally discontinuous functions in approximation space and preserves the energy conservation law. Both continuous and…