Discrete approximation of the solution of the Dirichlet problem by discrete means.
Discrete compactness for a discontinuous Galerkin approximation of Maxwell's system
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.
Discrete forms of Friedrichs' inequalities in the finite element method
Discrete maximum principle for interior penalty discontinuous Galerkin methods
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...
Discrete Sobolev and Poincaré inequalities for piecewise polynomial functions.
Discrete Sobolev inequalities and error estimates for finite volume solutions of convection diffusion equations
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.
Discrete Sobolev inequalities and Lp error estimates for finite volume solutions of convection diffusion equations
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.
Discrete Sobolev spaces and regularity of elliptic difference schemes
Discrete wavelet transforms accelerated sparse preconditioners for dense boundary element systems.
Discretization by Finite Elements of a Model Parameter Dependent Problem.
Discretization errors at free boundaries of the Grad-Schlüter-Shafranov equation.
Discretization methods with analytical characteristic methods for advection-diffusion-reaction equations and 2d applications
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...
Discretization of semicoercive variational inequalities.
Divergence boundary conditions for vector Helmholtz equations with divergence constraints
Divergence boundary conditions for vector Helmholtz equations with divergence constraints
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.
Divergence of FEM: Babuška-Aziz triangulations revisited
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....
Divergence stability in connection with the -version of the finite element method
Domain decomposition algorithms for first-order system least squares methods.
Domain decomposition algorithms for time-harmonic Maxwell equations with damping
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.
Domain Decomposition Algorithms for Time-Harmonic Maxwell Equations with Damping
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.