A Priori Error Estimates for Mixed Finite Element $\theta$-Schemes for the Wave Equation [PDF]
, 2015 A family of implicit-in-time mixed finite element schemes is presented for the numerical approximation of the acoustic wave equation. The mixed space discretization is based on the displacement form of the wave equation and the time-stepping method ...
Karaa, Samir
core +5 more sources
Robust equilibrated a posteriori error estimators for the Reissner-Mindlin system [PDF]
, 2010 We consider a conforming finite element approximation of the Reissner-Mindlin system. We propose a new robust a posteriori error estimator based on H(div) conforming finite elements and equilibrated fluxes.
Creusé, Emmanuel +2 more
core +4 more sources
Numerical Homogenization of the Acoustic Wave Equations with a Continuum of Scales [PDF]
, 2008 In this paper, we consider numerical homogenization of acoustic wave equations with heterogeneous coefficients, namely, when the bulk modulus and the density of the medium are only bounded.
Owhadi, Houman, Zhang, Lei
core +3 more sources
A class of Galerkin schemes for time-dependent radiative transfer [PDF]
, 2015 The numerical solution of time-dependent radiative transfer problems is challenging, both, due to the high dimension as well as the anisotropic structure of the underlying integro-partial differential equation.
Egger, Herbert, Schlottbom, Matthias
core +2 more sources
Galerkin and Runge–Kutta methods: unified formulation, a posteriori error estimates and nodal superconvergence [PDF]
, 2011 . We unify the formulation and analysis of Galerkin and Runge–Kutta methods for the time discretization of parabolic equations. This, together with the concept of reconstruction of the approximate solutions, allows us to establish a posteriori ...
A. Lozinski +21 more
core +5 more sources
East Asian Journal on Applied Mathematics, 2019 A spatial compact difference scheme for a class of fourth-order temporal multi-term fractional wave equations is developed. The original problem is reduced to a lower order system and the corresponding time fractional derivatives are approximated by the ...
Guang‐hua Gao, Rui Liu
semanticscholar +1 more source
Robust error estimates in weak norms for advection dominated transport problems with rough data [PDF]
, 2014 We consider mixing problems in the form of transient convection--diffusion equations with a velocity vector field with multiscale character and rough data.
Burman, Erik
core +2 more sources
On well-separated sets and fast multipole methods
, 2011 The notion of well-separated sets is crucial in fast multipole methods as the main idea is to approximate the interaction between such sets via cluster expansions.
Engblom, Stefan
core +1 more source
An Efficient Spectral Petrov-Galerkin Method for Nonlinear Hamiltonian Systems
Communications in Computational Physics, 2019 In this paper, an efficient spectral Petrov-Galerkin time-stepping method for solving nonlinear Hamiltonian systems is presented and studied. Conservation properties of the proposed method (including symplectic structure preserving and energy ...
Jing An
semanticscholar +1 more source
Superconvergence of a discontinuous Galerkin method for fractional diffusion and wave equations [PDF]
, 2012 We consider an initial-boundary value problem for $\partial_tu-\partial_t^{-\alpha}\nabla^2u=f(t)$, that is, for a fractional diffusion ...
Eriksson K. +2 more
core +1 more source