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Displaying 1341 –
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1417
We semi-discretize in space a time-dependent Navier-Stokes system on a three-dimensional polyhedron by finite-elements schemes defined on two grids. In the first step, the fully non-linear problem is semi-discretized on a coarse grid, with mesh-size . In the second step, the problem is linearized by substituting into the non-linear term, the velocity computed at step one, and the linearized problem is semi-discretized on a fine grid with mesh-size . This approach is motivated by the fact that,...
We semi-discretize in space a time-dependent Navier-Stokes system
on a three-dimensional polyhedron by finite-elements schemes
defined on two grids. In the first step, the fully non-linear
problem is semi-discretized on a coarse grid, with mesh-size H.
In the second step, the problem is linearized by substituting
into the non-linear term, the velocity uH computed at step
one, and the linearized problem is semi-discretized on a fine
grid with mesh-size h. This approach is motivated by the fact
that,...
In this article, we present a new two-level stabilized nonconforming finite elements method for the two dimensional Stokes problem. This method is based on a local Gauss integration technique and the mixed nonconforming finite element of the pair (nonconforming linear element for the velocity, conforming linear element for the pressure). The two-level stabilized finite element method involves solving a small stabilized Stokes problem on a coarse mesh with mesh size and a large stabilized Stokes...
The convergence of a two-scale FEM for elliptic problems in divergence form with coefficients and geometries oscillating at length scale is analyzed. Full elliptic regularity independent of is shown when the solution is viewed as mapping from the slow into the fast scale. Two-scale FE spaces which are able to resolve the scale of the solution with work independent of and without analytical homogenization are introduced. Robust in error estimates for the two-scale FE spaces are proved....
The convergence of a two-scale FEM for elliptic problems in
divergence form with coefficients and geometries oscillating at
length scale ε << 1 is analyzed.
Full elliptic regularity independent of ε is shown
when the solution is viewed as mapping from the slow into the fast scale.
Two-scale FE spaces which are able to resolve the ε scale of the
solution with work independent of ε and without
analytical homogenization are introduced. Robust
in ε error estimates for the two-scale FE spaces...
The paper is devoted to verification of accuracy of approximate solutions obtained in computer simulations. This problem is strongly related to a posteriori error estimates, giving computable bounds for computational errors and detecting zones in the solution domain where such errors are too large and certain mesh refinements should be performed. A mathematical model consisting of a linear elliptic (reaction-diffusion) equation with a mixed Dirichlet/Neumann/Robin boundary condition is considered...
This article presents an idea in the finite element methods (FEMs) for obtaining two-sided bounds of exact eigenvalues. This approach is based on the combination of nonconforming methods giving lower bounds of the eigenvalues and a postprocessing technique using conforming finite elements. Our results hold for the second and fourth-order problems defined on two-dimensional domains. First, we list analytic and experimental results concerning triangular and rectangular nonconforming elements which...
We derive an optimal lower bound of the interpolation error for linear finite elements on a bounded two-dimensional domain. Using the supercloseness between the linear interpolant of the true solution of an elliptic problem and its finite element solution on uniform partitions, we further obtain two-sided a priori bounds of the discretization error by means of the interpolation error. Two-sided bounds for bilinear finite elements are given as well. Numerical tests illustrate our theoretical analysis....
We derive an optimal lower bound of the
interpolation error for linear finite elements on a bounded two-dimensional
domain. Using the supercloseness between the linear interpolant
of the true solution of an elliptic problem and its finite element
solution on uniform partitions, we further
obtain two-sided a priori bounds of the discretization error by means of the
interpolation error. Two-sided bounds for bilinear finite elements
are given as well. Numerical tests illustrate our theoretical
analysis.
...
Mathematical treatment of a planar magnetic field excited by permanent magnets is presented. A special two-sided condition for differential magnetic reluctivity is introduced to prove the unique existence of both the weak and the approximate solutions and also a certain error estimate. Notes to numerical algorithm and practical applications are given.
In this note we study the periodic homogenization problem for a particular bidimensional selfadjoint elliptic operator of the second order. Theoretical and numerical considerations allow us to conjecture explicit formulae for the coefficients of the homogenized operator.
In this paper, we consider second order neutrons diffusion problem with
coefficients in L∞(Ω). Nodal method of the lowest
order is applied to approximate the problem's solution. The approximation
uses special basis functions [1] in which the coefficients
appear. The rate of convergence obtained is O(h2) in L2(Ω),
with a free rectangular triangulation.
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