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The Navier–Stokes equations are approximated by means of
a fractional step, Chorin–Temam projection method; the time derivative
is approximated by a three-level backward finite difference, whereas
the approximation in space is performed by a Galerkin technique.
It is shown that the proposed scheme yields an error
of
for the velocity in the norm of l2(L2(Ω)d), where l ≥ 1 is
the polynomial degree of the velocity approximation. It is also shown
that the splitting error of projection schemes based...
This work is devoted to the
analysis of a viscous finite-difference space semi-discretization
of a locally damped wave equation in a regular 2-D domain. The
damping term is supported in a suitable subset of the domain, so
that the energy of solutions of the damped continuous wave
equation decays exponentially to zero as time goes to infinity.
Using discrete multiplier techniques, we prove that adding a
suitable vanishing numerical viscosity term leads to a uniform
(with respect to the mesh size)...
In this paper, we consider the approximation of second order evolution equations. It is well known that the approximated system by finite element or finite difference is not uniformly exponentially or polynomially stable with respect to the discretization parameter, even if the continuous system has this property. Our goal is to damp the spurious high frequency modes by introducing numerical viscosity terms in the approximation scheme. With these viscosity terms, we show the exponential or polynomial...
We consider the approximation of a class of
exponentially stable infinite dimensional linear systems modelling
the damped vibrations of one dimensional vibrating systems or of
square plates. It is by now well known that the approximating
systems obtained by usual finite element or finite difference are
not, in general, uniformly stable with respect to the discretization
parameter. Our main result shows that, by adding a suitable
numerical viscosity term in the numerical scheme, our approximations
are...
Unique solvability and stability analysis is conducted for a generalized particle method for a Poisson equation with a source term given in divergence form. The generalized particle method is a numerical method for partial differential equations categorized into meshfree particle methods and generally indicates conventional particle methods such as smoothed particle hydrodynamics and moving particle semi-implicit methods. Unique solvability is derived for the generalized particle method for the...
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