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Displaying 481 –
500 of
1417
We propose a discontinuous Galerkin method for linear
elasticity, based on discontinuous piecewise linear approximation
of the displacements. We show optimal order a priori error estimates,
uniform in the incompressible limit, and thus locking is avoided.
The discontinuous Galerkin method is closely related to the
non-conforming Crouzeix–Raviart (CR) element, which in fact is
obtained when one of the stabilizing parameters tends to infinity.
In the case of the elasticity operator, for...
In this article we study discontinuous Galerkin finite element discretizations of linear
second-order elliptic partial differential equations with Dirac delta right-hand side. In
particular, assuming that the underlying computational mesh is quasi-uniform, we derive an
a priori bound on the error measured in terms of the
L2-norm. Additionally, we develop residual-based a
posteriori error estimators that can be used within an adaptive mesh refinement
...
In this article we study discontinuous Galerkin finite element discretizations of linear
second-order elliptic partial differential equations with Dirac delta right-hand side. In
particular, assuming that the underlying computational mesh is quasi-uniform, we derive an
a priori bound on the error measured in terms of the
L2-norm. Additionally, we develop residual-based a
posteriori error estimators that can be used within an adaptive mesh refinement
...
The evolution of n–dimensional graphs under a
weighted curvature flow is approximated by linear finite elements. We obtain
optimal error bounds for the normals and the normal velocities of the surfaces
in natural norms.
Furthermore we prove a global existence result for the
continuous problem and present some examples of computed surfaces.
In this paper we prove the discrete compactness property for
a discontinuous Galerkin approximation of Maxwell's system
on quite general tetrahedral meshes.
As a consequence, a discrete Friedrichs inequality is obtained
and the convergence of the discrete eigenvalues to the continuous ones is deduced
using the theory of collectively compact operators.
Some numerical experiments confirm the theoretical predictions.
A class of linear elliptic operators has an important qualitative property, the so-called maximum principle. In this paper we investigate how this property can be preserved on the discrete level when an interior penalty discontinuous Galerkin method is applied for the discretization of a 1D elliptic operator. We give mesh conditions for the symmetric and for the incomplete method that establish some connection between the mesh size and the penalty parameter. We then investigate the sharpness of...
The topic of this work is to obtain discrete Sobolev inequalities for piecewise constant functions, and to deduce error estimates on the approximate solutions of convection diffusion equations by finite volume schemes.
The topic of this work is to obtain discrete Sobolev inequalities for
piecewise constant functions, and to deduce Lp error estimates
on the approximate solutions of convection diffusion equations by finite
volume schemes.
Our studies are motivated by a desire to model long-time simulations of possible scenarios for a waste disposal. Numerical methods are
developed for solving the arising systems of convection-diffusion-dispersion-reaction
equations, and the received results of several discretization
methods are presented. We concentrate on linear reaction systems, which
can be solved analytically.
In the numerical methods, we use large time-steps to achieve
long simulation times of about 10 000 years.
We propose...
The idea of replacing a divergence constraint by a divergence boundary
condition is investigated. The connections between the formulations are
considered in detail. It is shown that the most common methods of using
divergence boundary conditions do not always work properly. Necessary
and sufficient conditions for the equivalence of the formulations are
given.
By re-examining the arguments and counterexamples in I. Babuška, A. K. Aziz (1976) concerning the well-known maximum angle condition, we study the convergence behavior of the linear finite element method (FEM) on a family of distorted triangulations of the unit square originally introduced by H. Schwarz in 1880. For a Poisson problem with polynomial solution, we demonstrate arbitrarily slow convergence as well as failure of convergence if the distortion of the triangulations grows sufficiently fast....
Three non-overlapping domain decomposition methods are proposed for the numerical approximation of time-harmonic Maxwell equations with damping (i.e., in a conductor). For each method convergence is proved and, for the discrete problem, the rate of convergence of the iterative algorithm is shown to be independent of the number of degrees of freedom.
Three non-overlapping domain decomposition methods are proposed for the
numerical
approximation of time-harmonic Maxwell equations with damping (i.e., in a conductor). For
each method convergence is proved and, for the discrete problem, the rate of
convergence
of the iterative algorithm is shown to be independent of the number of
degrees of freedom.
Currently displaying 481 –
500 of
1417