Related papers: A Galerkin least-square stabilisation technique fo…
We propose a state redistribution method for high order discontinuous Galerkin methods on curvilinear embedded boundary grids. State redistribution relaxes the overly restrictive CFL condition that results from arbitrarily small cut cells…
This paper presents a simplified weak Galerkin (WG) finite element method for solving biharmonic equations avoiding the use of traditional stabilizers. The proposed WG method supports both convex and non-convex polytopal elements in finite…
This paper considers weak Galerkin finite element approximations for a quasistatic Maxwell viscoelastic model. The spatial discretization uses piecewise polynomials of degree $k \ (k\geq 1)$ for the stress approximation, degree $k+1$ for…
We design an arbitrary high-order accurate nodal discontinuous Galerkin spectral element approximation for the nonlinear two dimensional shallow water equations with non-constant, possibly discontinuous, bathymetry on unstructured, possibly…
This paper proposes and analyzes a class of new weak Galerkin (WG) finite element methods for 2- and 3-dimensional linear elasticity problems. The methods use discontinuous piecewise-polynomial approximations of degrees $k(\geq 0)$ for the…
In two and three dimension we analyze discontinuous Galerkin methods for the acoustic problem. The acoustic fluid that we consider on this paper is inviscid, leading to a linear eigenvalue problem. The acoustic problem is written, in first…
This paper presents a high-order discontinuous Galerkin (DG) scheme for the simulation of wave propagation through coupled elastic-acoustic media. We use a first-order stress-velocity formulation, and derive a simple upwind-like numerical…
We present a few--mode Galerkin model for convection in binary fluid layers subject to an approximation to realistic horizontal boundary conditions at positive separation ratios. The model exhibits convection patterns in form of rolls and…
This paper concerns preservation of velocity and pressure equilibria in smooth, compressible, multicomponent flows in the inviscid limit. First, we derive the velocity-equilibrium and pressure-equilibrium conditions of a standard…
We formulate a numerical method for solving the two-phase flow poroelasticity equations. The scheme employs the interior penalty discontinuous Galerkin method and a sequential time-stepping method. The unknowns are the phase pressures and…
We investigate the propagation of uncertainties in the Aw-Rascle-Zhang model, which belongs to a class of second order traffic flow models described by a system of nonlinear hyperbolic equations. The stochastic quantities are expanded in…
A stabilizer free weak Galerkin (WG) finite element method on polytopal mesh has been introduced in Part I of this paper (J. Comput. Appl. Math, 371 (2020) 112699. arXiv:1906.06634.) Removing stabilizers from discontinuous finite element…
When nonconforming discontinuous Galerkin methods are implemented for hyperbolic equations using quadrature, exponential energy growth can result even when the underlying scheme with exact integration does not support such growth. Using…
Stable and accurate finite element methods are presented for Darcy flow in heterogeneous porous media with an interface of discontinuity of the hydraulic conductivity tensor. Accurate velocity fields are computed through global or local…
We propose a new discrete element method supporting general polyhedral meshes. The method can be understood as a lowest-order discontinuous Galerkin method parametrized by the continuous mechanical parameters (Young's modulus and Poisson's…
We investigate the accuracy and robustness of one of the most common methods used in glaciology for the discretization of the $\mathfrak{p}$-Stokes equations: equal order finite elements with Galerkin Least-Squares (GLS) stabilization.…
In this article a theoretical framework for problems involving fractional equations of hyperbolic type arising in the theory of viscoelasticity is presented. Based on the Galerkin method, a variational problem of the fractionary…
Stochastic Galerkin formulations of the two-dimensional shallow water systems parameterized with random variables may lose hyperbolicity, and hence change the nature of the original model. In this work, we present a hyperbolicity-preserving…
This work presents a novel stabilization strategy for the Galerkin formulation of the incompressible Navier-Stokes equations, developed to achieve high accuracy while ensuring convergence and compatibility with high-order elements on…
We give an a posteriori analysis of a semi-discrete discontinuous Galerkin scheme approximating solutions to a model of multiphase elastodynamics, which involves an energy density depending not only on the strain but also the strain…