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Abstract: We present a discontinuous Galerkin method for the plate problem. The method employs a discontinuous approximation space allowing nonmatching grids and different types of approximation spaces. Continuity is enforced weakly through the variational form. Discrete approximations of the normal and twisting moments and the transversal force, which satisfy the equilibrium condition on an element...
Abstract: A popular method for the discretization of conservation laws is the finite volume (FV) method, used extensively in CFD, based on piecewise constant approximation of the solution sought. However, the FV method has problems with the approximation of diffusion terms. Therefore, in several works [1719, 1, 12, 16, 2], a combination of the FV and FE methods is used. To this end, it is necessary...
Abstract: This paper is concerned with the numerical solution of a -rational SturmLiouville problem. Classical methods are considered in connection with the shooting technique used via the method of Magnus series and boundary value methods. We prove that, in the presence of an eigenvalue embedded in the essential spectrum, these methods exhibit a decay in their performance. Nevertheless some boundary...
Abstract: We consider the coupling of dual-mixed finite element and boundary element methods to solve a linear-nonlinear transmission problem in plane hyperelasticity with mixed boundary conditions. Besides the displacement and the stress tensor, we introduce the strain tensor as an additional unknown, which yields a two-fold saddle point operator equation as the corresponding variational formulation...
Abstract: Two different stabilization procedures for mixed finite element schemes for ReissnerMindlin plate problems are introduced. They are based on a suitable modification of the discrete shear energy like that introduced when a partial selective reduced integration technique is used. Some numerical results will be presented in order to show the performance of these schemes with respect to the...
Abstract: Underflow is a floating-point phenomenon. Although the use of gradual underflow as defended in [2] and [3] is now widespread, most numerical analysts may not be aware of the fact that several implementations of the same principle are in existence, leading to different behavior of code on different platforms, mainly with respect to exception signaling. We intend to thoroughly discuss the...
Abstract: Mixed and componentwise condition numbers are useful in understanding stability properties of algorithms for solving structured linear systems. The DFT (discrete Fourier transform) is an essential building block of these algorithms. We obtain estimates of mixed and componentwise condition numbers of the DFT. To this end, we explicitly compute certain special vectors that share with their...
Abstract: Any solution of the incompressible NavierStokes equations in three-dimensional domains with edges has anisotropic singular behaviour which is treated numerically by using anisotropic finite element meshes. The velocity is approximated by CrouzeixRaviart (nonconforming 1) elements and the pressure by piecewise constants. This method is stable for general meshes since the inf-sup condition...
Abstract: Domain decomposition techniques provide a powerful tool for the numerical approximation of partial differential equations. Here, we consider mortar techniques for quadratic finite elements. In particular, we focus on dual Lagrange multiplier spaces. These non-standard Lagrange multiplier spaces yield optimal discretization schemes and a locally supported basis for the associated constrained...
Abstract: In this note, we show that, in the one-dimensional case, as an approximation to residual-free bubbles (RFB), certain practical bubbles can be applied to obtain a scheme which is uniformly convergent with respect to small viscosity in the energy norm for advection-diffusion problems.
Abstract: We describe a stable algorithm, having linear complexity, for the solution of banded-plus-semiseparable linear systems. The algorithm exploits the structural properties of the inverse of a semiseparable matrix. Stability is achieved by combining these properties with partial pivoting techniques. Several numerical experiments are shown to confirm the effectiveness of the proposed approach.
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