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Displaying 141 –
160 of
287
The present paper deals with a finite element approximation of partial differential equations when the domain is decomposed into sub-domains which are meshed independently. The method we obtain is never conforming because the continuity constraints on the boundary of the sub-domains are not imposed strongly but only penalized. We derive a selection rule for the penalty parameter which ensures a quasi-optimal convergence.
The present paper deals with a finite element approximation of partial differential equations when the
domain is decomposed into sub-domains which are meshed independently. The method we obtain is never conforming
because the continuity constraints on the boundary of the sub-domains are not imposed strongly but only penalized.
We derive a selection rule for the penalty parameter which ensures a quasi-optimal convergence.
This work is focused on a weak solution of a coupled physical task of the microwave wood drying process with stress-strain effects and moisture/temperature dependency. Due to the well known weak solutions for the individual physical fields, the author concerns with the coupled stress-strain relation coupled with the moisture and temperature distributions. For the scale dependency the subgrid upscaling method was used.
The solved region is assumed to be divided into discontinuous subregions
according...
A two-dimensional depth-averaged flow and temperature model was applied to study the circulation patterns in the Oder (Szczecin) Lagoon located on the border between Germany and Poland. The system of shallow water and temperature evolution equations is discretized with the modified Utnes scheme [4], which is characterized by a semi-decoupling algorithm. The continuity equation is rearranged to Helmholtz equation form. The upwinding Tabata method [3] is used to approximate convective terms. Averaged...
We deal with modelling of flows in channels or tubes with abrupt changes of the diameter. The goal of this work is to construct the FEM solution in the vicinity of these corners as precise as desired. We present two ways. The first approach makes use of a posteriori error estimates and the adaptive strategy. The second approach is based on the asymptotic behaviour of the exact solution in the vicinity of the corner and on the a priori error estimate of the FEM solution. Then we obtain the solution...
Existence and finite element approximation of a hyperbolic-parabolic problem is studied. The original two-dimensional domain is approximated by a polygonal one (external approximations). The time discretization is obtained using Euler’s backward formula (Rothe’s method). Under certain smoothing assumptions on the data (see (2.6), (2.7)) the existence and uniqueness of the solution and the convergence of Rothe’s functions in the space is proved.
In this paper we present a weak formulation of a two-dimensional stationary heat conduction problem with the radiation boundary condition. The problem can be described by an operator which is monotone on the convex set of admissible functions. The relation between classical and weak solutions as well as the convergence of the finite element method to the weak solution in the norm of the Sobolev space are examined.
The paper is devoted to the numerical modelling of a subsonic irrotational nonviscous flow past a cascade of profiles in a variable thickness fluid layer. It leads to a nonlinear two-dimensional elliptic problem with nonstandard nonhomogeneous boundary conditions. The problem is discretized by the finite element method. Both theoretical and practical questions of the finite element implementation are studied; convergence of the method, numerical integration, iterative methods for the solution of...
In part I of the paper (see Zlámal [13]) finite element solutions of the nonstationary semiconductor equations were constructed. Two fully discrete schemes were proposed. One was nonlinear, the other partly linear. In this part of the paper we justify the nonlinear scheme. We consider the case of basic boundary conditions and of constant mobilities and prove that the scheme is unconditionally stable. Further, we show that the approximate solution, extended to the whole time interval as a piecewise...
The finite element method for a strongly elliptic mixed boundary value problem is analyzed in the domain whose boundary is formed by two circles , with the same center and radii , , where . On one circle the homogeneous Dirichlet boundary condition and on the other one the nonhomogeneous Neumann boundary condition are prescribed. Both possibilities for are considered. The standard finite elements satisfying the minimum angle condition are in this case inconvenient; thus triangles obeying...
This paper presents a computational procedure for the design of an observer of a nonlinear system. Outputs can be delayed, however, this delay must be known and constant. The characteristic feature of the design procedure is computation of a solution of a partial differential equation. This equation is solved using the finite element method. Conditions under which existence of a solution is guaranteed are derived. These are formulated by means of theory of partial differential equations in -space....
Currently displaying 141 –
160 of
287