186 research outputs found
Numerical methods for hyperbolic and parabolic integro-differential equations
An analysis by energy methods is given for fully discrete numerical methods for time-dependent partial integro-differential equations. Stability and error estimates are derived in H1 and L2. The methods considered pay attention to the storage needs during time-stepping
Maximum norm error estimates in the finite element method with isoparametric quadratic elements and numerical integration
Validation of the A Posteriori Error Estimator Based on Polynomial Preserving Recovery for Linear Elements
In this paper the quality of the error estimator based on the Polynomial Preserving Recovery (PPR) is investigated using the computer-based approach proposed by Babiiska et al. A comparison is made between the error estimator based on the PPR and the one based on the Superconvergence Patch Recovery (SPR). It was found that the PPR is at least as good as the SPR
Weighted Sobolev spaces and regularity for polyhedral domains
We prove a regularity result for the Poisson problem , u
|\_{\pa \PP} = g on a polyhedral domain \PP \subset \RR^3 using the \BK\
spaces \Kond{m}{a}(\PP). These are weighted Sobolev spaces in which the
weight is given by the distance to the set of edges \cite{Babu70,
Kondratiev67}. In particular, we show that there is no loss of
\Kond{m}{a}--regularity for solutions of strongly elliptic systems with
smooth coefficients. We also establish a "trace theorem" for the restriction to
the boundary of the functions in \Kond{m}{a}(\PP)
A Toy Model for Testing Finite Element Methods to Simulate Extreme-Mass-Ratio Binary Systems
Extreme mass ratio binary systems, binaries involving stellar mass objects
orbiting massive black holes, are considered to be a primary source of
gravitational radiation to be detected by the space-based interferometer LISA.
The numerical modelling of these binary systems is extremely challenging
because the scales involved expand over several orders of magnitude. One needs
to handle large wavelength scales comparable to the size of the massive black
hole and, at the same time, to resolve the scales in the vicinity of the small
companion where radiation reaction effects play a crucial role. Adaptive finite
element methods, in which quantitative control of errors is achieved
automatically by finite element mesh adaptivity based on posteriori error
estimation, are a natural choice that has great potential for achieving the
high level of adaptivity required in these simulations. To demonstrate this, we
present the results of simulations of a toy model, consisting of a point-like
source orbiting a black hole under the action of a scalar gravitational field.Comment: 29 pages, 37 figures. RevTeX 4.0. Minor changes to match the
published versio
A linearized implicit pseudo-spectral method for some model equations: the regularized long wave equations
Finite Element Methods for Elliptic Distributed Optimal Control Problems with Pointwise State Constraints
Finite element methods for a model elliptic distributed optimal control
problem with pointwise state constraints are considered from the perspective of
fourth order boundary value problems
Lp-estimates for Friedrichs1 scheme for strongly hyperbolic systems in two space variables.
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