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Displaying 541 –
560 of
1956
Finite element methods with piecewise polynomial spaces in space for solving the nonstationary heat equation, as a model for parabolic equations are considered. The discretization in time is performed using the Crank-Nicolson method. A new a priori estimate is proved. Thanks to this new a priori estimate, a new error estimate in the discrete norm of is proved. An -error estimate is also shown. These error estimates are useful since they allow us to get second order time accurate approximations...
In this paper we present a novel exponentially fitted finite element
method with triangular elements for the decoupled continuity equations
in the drift-diffusion model of semiconductor devices.
The continuous problem is first formulated as a variational problem
using a weighted inner product. A Bubnov-Galerkin
finite element method with a set of piecewise exponential basis functions
is then proposed. The method is shown to be stable and can be regarded as
an extension to two dimensions of the...
In this paper a new finite element approach is presented which allows the discretization of PDEs on domains containing small micro-structures with extremely few degrees of freedom. The applications of these so-called Composite Finite Elements are two-fold. They allow the efficient use of multi-grid methods to problems on complicated domains where, otherwise, it is not possible to obtain very coarse discretizations with standard finite elements. Furthermore, they provide a tool for discrete homogenization...
We analyze a new formulation of the Stokes equations in three-dimensional axisymmetric geometries, relying on Fourier expansion with respect to the angular variable: the problem for each Fourier coefficient is two-dimensional and has six scalar unknowns, corresponding to the vector potential and the vorticity. A spectral discretization is built on this formulation, which leads to an exactly divergence-free discrete velocity. We prove optimal error estimates.
We analyze a new formulation of the Stokes equations in
three-dimensional axisymmetric geometries, relying on Fourier expansion with respect to
the angular variable: the problem for each Fourier coefficient is two-dimensional and has
six scalar unknowns, corresponding to the vector potential and the vorticity. A
spectral discretization is built on this formulation, which leads to an exactly
divergence-free discrete velocity. We prove optimal error estimates.
In this paper we construct a new H(div)-conforming projection-based p-interpolation operator that assumes only Hr(K) -1/2(div, K)-regularity (r > 0) on the reference element (either triangle or square) K. We show that this operator is stable...
In this paper we construct a new H(div)-conforming projection-based
p-interpolation operator that assumes only Hr(K) -1/2(div, K)-regularity
(r > 0) on the reference element (either triangle or square) K.
We show that this operator is stable with...
By properties of Cvetković-Kostić-Varga-type (or, for short, CKV-type) B-matrices, a new class of nonsingular matrices called CKV-type -matrices is given, and a new inclusion interval of the real eigenvalues of real matrices is presented. It is shown that the new inclusion interval is sharper than those provided by J. M. Peña (2003), and by H. B. Li et al. (2007). We also propose a direct algorithm for computing the new inclusion interval. Numerical examples are included to illustrate the effectiveness...
A new Kantorovich-type convergence theorem for Newton's method is established for approximating a locally unique solution of an equation F(x)=0 defined on a Banach space. It is assumed that the operator F is twice Fréchet differentiable, and that F', F'' satisfy Lipschitz conditions. Our convergence condition differs from earlier ones and therefore it has theoretical and practical value.
Currently displaying 541 –
560 of
1956