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
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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
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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
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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
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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
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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
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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
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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
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Linear-implicit strong schemes for Itô-Galkerin approximations of stochastic PDEs [PDF]
, 2010 Linear-implicit versions of strong Taylor numerical schemes for finite dimensional Itô stochastic differential equations (SDEs) are shown to have the same order as the original scheme.
Kloeden, Peter E., Shott, Stephen
core
Interior a posteriori error estimates for time discrete approximations of parabolic problems [PDF]
, 2012 a posteriori error estimates for time discrete approximations ...
Charalambos Makridakis +3 more
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