Finite element methods for nonlinear parabolic equations
Finite Element Methods for Nonlinear Shell Analysis.
Finite element methods for solving the stationary Stokes and Navier-Stokes equations
Finite Element Methods for Symmetric Hyperbolic Equations.
Finite element methods for the transport equation
Finite element methods on non-conforming grids by penalizing the matching constraint
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.
Finite element methods on non-conforming grids by penalizing the matching constraint
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.
Finite element solution of a hyperbolic-parabolic problem
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.
Finite element solution of a nonlinear diffusion problem with a moving boundary
Finite element solution of a nonlinear diffusion problem with a moving boundary
Finite element solution of a stationary heat conduction equation with the radiation boundary condition
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.
Finite Element Solution of Diffusion Problems with Irregular Data.
Finite element solution of flows through cascades of profiles in a layer of variable thickness
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...
Finite Element Solution of Nonlinear Elliptic Problems.
Finite element solution of quasistationary nonlinear magnetic field
Finite element solution of the fundamental equations of semiconductor devices. II
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...
Finite element solutions for radiation cooling problems with nonlinear boundary conditions
Finite element subspaces with optimal rates of convergence for the stationary Stokes problem
Finite Element Variational Crimes in Parabolic-Elliptic Problems. Part I. Nonlinear Schemes.
Finite element variational crimes in the case of semiregular elements
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...