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Displaying 581 –
600 of
1417
The Ultra Weak Variational Formulation (UWVF) of the Helmholtz equation
provides a variational framework suitable for discretization using plane wave solutions
of an appropriate adjoint equation. Currently convergence of the method is only proved
on the boundary of the domain. However substantial computational evidence
exists showing that the method also converges throughout the domain of the Helmholtz equation. In this paper we exploit the fact that the UWVF is essentially an upwind discontinuous...
In an error estimation of finite element solutions to the Poisson equation, we usually impose the shape regularity assumption on the meshes to be used. In this paper, we show that even if the shape regularity condition is violated, the standard error estimation can be obtained if ``bad'' elements that violate the shape regularity or maximum angle condition are covered virtually by simplices that satisfy the minimum angle condition. A numerical experiment illustrates the theoretical result.
This contribution is devoted to modeling damage zones caused by the excavation of tunnels and boreholes (EDZ zones) in connection with the issue of deep storage of spent nuclear fuel in crystalline rocks. In particular, elastic-plastic models with Mohr-Coulomb or Hoek-Brown yield criteria are considered. Selected details of the numerical solution to the corresponding problems are mentioned. Possibilities of elastic and elastic-plastic approaches are illustrated by a numerical example.
This paper derives upper and lower bounds for the -condition
number of the stiffness matrix resulting from the finite element
approximation of a linear, abstract model problem. Sharp estimates in
terms of the meshsize h are obtained. The theoretical results are
applied to finite element approximations of elliptic PDE's in
variational and in mixed form, and to first-order PDE's approximated
using the Galerkin–Least Squares technique or by
means of a non-standard Galerkin technique in
L1(Ω). Numerical...
In this paper, a nonlinear problem corresponding to a simplified Oldroyd-B model without convective terms is considered. Assuming the domain to be a convex polygon, existence of a solution is proved for small relaxation times. Continuous piecewise linear finite elements together with a Galerkin Least Square (GLS) method are studied for solving this problem. Existence and a priori error estimates are established using a Newton-chord fixed point theorem, a posteriori error estimates are also derived....
In this paper, a
nonlinear problem corresponding to a simplified Oldroyd-B model
without convective terms is considered. Assuming the domain to be a convex
polygon, existence of a solution
is proved for small relaxation times.
Continuous piecewise linear finite elements together with
a Galerkin Least Square (GLS) method are studied for solving this problem.
Existence and a priori error estimates
are established using a Newton-chord fixed point theorem,
a posteriori error estimates are also derived.
An...
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1417