相关论文: Multi-patch discontinuous Galerkin isogeometric an…
In this paper we analyze the error as well for the semi-discretization as the full discretization of a time-dependent convection-diffusion problem. We use for the discretization in space the local discontinuous Galerkin (LDG) method on a…
This work introduces a novel discontinuity-tracking framework for resolving discontinuous solutions of conservation laws with high-order numerical discretizations that support inter-element solution discontinuities, such as discontinuous…
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…
This work presents a novel methodology for speeding up the assembly of stiffness matrices for laminate composite 3D structures in the context of isogeometric and finite element discretizations. By splitting the involved terms into their…
In this contribution, we extend the hybridization framework for the Hodge Laplacian [Awanou et al., Hybridization and postprocessing in finite element exterior calculus, 2023] to port-Hamiltonian systems describing linear wave propagation…
In this article, we propose a modified nonlinear Schr\"odinger equation for modeling pulse propagation in optical waveguides. The proposed model bifurcates into a system of elliptic and hyperbolic equations depending on waveguide…
In this article, we discuss the efficient implementation of powerful domain decomposition smoothers for multigrid methods for high order discontinuous Galerkin (DG) finite element methods. In particular, we study the inversion of matrices…
In this article we investigate a finite element formulation of strongly monotone quasi-linear elliptic PDEs in the context of fixed-point iterations. As opposed to Newton's method, which requires information from the previous iteration in…
We design and analyze a Schwarz waveform relaxation algorithm for domain decomposition of advection-diffusion-reaction problems with strong heterogeneities. The interfaces are curved, and we use optimized Robin or Ventcell transmission…
We consider the numerical discretization of the time-domain Maxwell's equations with an energy-conserving discontinuous Galerkin finite element formulation. This particular formulation allows for higher order approximations of the electric…
In this paper, we study a mixed discontinuous Galerkin (MDG) method to solve linear elasticity problem with arbitrary order discontinuous finite element spaces in $d$-dimension ($d=2,3$). This method uses polynomials of degree $k+1$ for the…
In this work, we study the approximation properties of multi-patch dG-IgA methods, that apply the multipatch Isogeometric Analysis (IgA) discretization concept and the discontinuous Galerkin (dG) technique on the interfaces between the…
This paper analyzes a space-time finite element method for fractional wave problems. The method uses a Petrov-Galerkin type time-stepping scheme to discretize the time fractional derivative of order $ \gamma $ ($1<\gamma<2$). We establish…
Discretizing a solution in the Fourier domain rather than the time domain presents a significant advantage in solving transport problems that vary smoothly and periodically in time, such as cardiorespiratory flows. The finite element…
We present a stable discontinuous Galerkin (DG) method with a perfectly matched layer (PML) for three and two space dimensional linear elastodynamics, in velocity-stress formulation, subject to well-posed linear boundary conditions. First,…
Certain energy-conservative Galerkin discretizations for nonlinear dispersive wave equations have revealed an unusual convergence behavior: optimal convergence is attained when continuous Lagrange finite element spaces of odd polynomial…
We introduce a new hybridized discontinuous Galerkin method for the incompressible magnetohydrodynamics equations. If particular velocity, pressure, magnetic field, and magnetic pressure spaces are employed for both element and trace…
We introduce a family of mixed methods and discontinuous Galerkin discretisations designed to numerically solve the Oseen equations written in terms of velocity, vorticity, and Bernoulli pressure. The unique solvability of the continuous…
Continuum computational kinetic plasma models evolve the distribution function of a plasma species $f_s$ on a phase-space grid over time. In many problems of interest the distribution function has limited extent in velocity space; hence,…
An integro-differential equation, modeling dynamic fractional order viscoelasticity, with a Mittag-Leffler type convolution kernel is considered. A discontinuous Galerkin method, based on piecewise constant polynomials is formulated for…