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Displaying 61 –
80 of
1240
In this paper, we present extensive numerical tests showing the performance
and robustness of a Balancing Neumann-Neumann method for the solution of algebraic linear systems arising from hp finite element approximations of scalar elliptic
problems on geometrically refined boundary layer meshes in
three dimensions. The numerical results are in good agreement with the theoretical bound for the condition number of the preconditioned operator derived in [Toselli and Vasseur, IMA J. Numer. Anal.24 (2004)...
We formulate and study numerically a new, parameter-free stabilized finite element method for advection-diffusion problems. Using properties of compatible finite element spaces we establish connection between nodal diffusive fluxes and one-dimensional diffusion equations on the edges of the mesh. To define the stabilized method we extend this relationship to the advection-diffusion case by solving simplified one-dimensional versions of the governing equations on the edges. Then we use H(curl)-conforming...
A general construction of test functions in the Petrov-Galerkin method is described. Using this construction; algorithms for an approximate solution of the Dirichlet problem for the differential equation are presented and analyzed theoretically. The positive number is supposed to be much less than the discretization step and the values of . An algorithm for the corresponding two-dimensional problem is also suggested and results of numerical tests are introduced.
We introduce a piecewise P2-nonconforming quadrilateral finite element. First, we decompose a convex quadrilateral into the union of four triangles divided by its diagonals. Then the finite element space is defined by the set of all piecewise P2-polynomials that are quadratic in each triangle and continuously differentiable on the quadrilateral. The degrees of freedom (DOFs) are defined by the eight values at the two Gauss points on each of the four edges plus the value at the intersection of the...
We derive a residual-based a posteriori error estimator for a discontinuous Galerkin approximation of the Steklov eigenvalue problem. Moreover, we prove the reliability and efficiency of the error estimator. Numerical results are provided to verify our theoretical findings.
We present new a posteriori error estimates for the finite volume approximations
of elliptic problems. They are obtained by applying functional a posteriori
error estimates to natural extensions of the approximate solution and its flux
computed by the finite volume method. The estimates give guaranteed upper bounds
for the errors in terms of the primal (energy) norm, dual norm (for fluxes), and
also in terms of the combined primal-dual norms. It is shown that the estimates
provide sharp upper and...
For a nonconforming finite element approximation of an elliptic model problem, we propose a posteriori error estimates in the energy norm which use as an additive term the “post-processing error” between the original nonconforming finite element solution and an easy computable conforming approximation of that solution. Thus, for the error analysis, the existing theory from the conforming case can be used together with some simple additional arguments. As an essential point, the property is exploited...
For a nonconforming finite element approximation of an elliptic model
problem, we propose a posteriori error estimates in the energy norm
which use as an additive term the “post-processing error” between
the original nonconforming finite element solution and an easy
computable conforming approximation of that solution.
Thus, for the error analysis, the existing theory from the conforming
case can be used together with some simple additional arguments.
As an essential point, the property is...
In this paper, we consider mortar-type Crouzeix-Raviart element discretizations for second order elliptic problems with discontinuous coefficients. A preconditioner for the FETI-DP method is proposed. We prove that the condition number of the preconditioned operator is bounded by , where and are mesh sizes. Finally, numerical tests are presented to verify the theoretical results.
Domain decomposition techniques provide a flexible tool for the numerical approximation of partial differential equations. Here, we consider mortar techniques for quadratic finite elements in 3D with different Lagrange multiplier spaces. In particular, we focus on Lagrange multiplier spaces which yield optimal discretization schemes and a locally supported basis for the associated constrained mortar spaces in case of hexahedral triangulations. As a result, standard efficient iterative solvers as...
Currently displaying 61 –
80 of
1240