Caractéristiques d'approximation des compacts dans les espaces fonctionnels et problèmes aux limites elliptiques
Compatibilité des espaces discrets pour l'approximation spectrale du problème de Stokes périodique/non périodique
Computer implementation of a coupled boundary and finite element methods for the steady exterior Oseen problem.
Convergence analysis for an exponentially fitted Finite Volume Method
The paper is devoted to the convergence analysis of a well-known cell-centered Finite Volume Method (FVM) for a convection-diffusion problem in . This FVM is based on Voronoi boxes and exponential fitting. To prove the convergence of the FVM, we use a new nonconforming Petrov-Galerkin Finite Element Method (FEM) for which the system of linear equations coincides completely with that of the FVM. Thus, by proving convergence properties of the FEM we obtain similar ones for the FVM. For the error...
Convergence of approximate solutions to scalar conservation laws by degenerate diffusion
Convergent algorithms suitable for the solution of the semiconductor device equations
In this paper, two algorithms are proposed to solve systems of algebraic equations generated by a discretization procedure of the weak formulation of boundary value problems for systems of nonlinear elliptic equations. The first algorithm, Newton-CG-MG, is suitable for systems with gradient mappings, while the second, Newton-CE-MG, can be applied to more general systems. Convergence theorems are proved and application to the semiconductor device modelling is described.
Curved triangular finite -elements
Curved triangular -elements which can be pieced together with the generalized Bell’s -elements are constructed. They are applied to solving the Dirichlet problem of an elliptic equation of the order in a domain with a smooth boundary by the finite element method. The effect of numerical integration is studied, sufficient conditions for the existence and uniqueness of the approximate solution are presented and the rate of convergence is estimated. The rate of convergence is the same as in the...
Deterministic multivariate model for simulation of downstream BIVAL automatic controller in irrigation systems.
Domain optimization in -axisymmetric elliptic problems by dual finite element method
An axisymmetric second order elliptic problem with mixed boundary conditions is considered. The shape of the domain has to be found so as to minimize a cost functional, which is given in terms of the cogradient of the solution. A new dual finite element method is used for approximate solutions. The existence of an optimal domain is proven and a convergence analysis presented.
Domain optimization in axisymmetric elliptic boundary value problems by finite elements
An axisymmetric second order elliptic problem with mixed boundary conditions is considered. A part of the boundary has to be found so as to minimize one of four types of cost functionals. The existence of an optimal boundary is proven and a convergence analysis for piecewise linear approximate solutions presented, using weighted Sobolev spaces.
Dual variational principles for an elliptic partial differential equation
Einige Eigenschaften der Lösung der Wellengleichung mit der Korrektion von Rayleigh
Éléments finis et problèmes elliptiques dégénérés
Exact, approximate solutions and error bounds for coupled implicit systems of partial differential equations.
Exact solutions for the generalized BBM equation with variable coefficients.
Existence and Approximation of Solutions of Non-Linear Elliptic Equations.
Existenzsätze mit der Linienmethode für Parabolische Probleme und periodische Lösungen von ut = f(t,x,u,ux,uxx).
Extensions from the Sobolev spaces satisfying prescribed Dirichlet boundary conditions
Extensions from into (where ) are constructed in such a way that extended functions satisfy prescribed boundary conditions on the boundary of . The corresponding extension operator is linear and bounded.
Flux-upwind stabilization of the discontinuous Petrov–Galerkin formulation with Lagrange multipliers for advection-diffusion problems
In this work we consider the dual-primal Discontinuous Petrov–Galerkin (DPG) method for the advection-diffusion model problem. Since in the DPG method both mixed internal variables are discontinuous, a static condensation procedure can be carried out, leading to a single-field nonconforming discretization scheme. For this latter formulation, we propose a flux-upwind stabilization technique to deal with the advection-dominated case. The resulting scheme is conservative and satisfies a discrete maximum...
Flux-upwind stabilization of the discontinuous Petrov–Galerkin formulation with Lagrange multipliers for advection-diffusion problems
In this work we consider the dual-primal Discontinuous Petrov–Galerkin (DPG) method for the advection-diffusion model problem. Since in the DPG method both mixed internal variables are discontinuous, a static condensation procedure can be carried out, leading to a single-field nonconforming discretization scheme. For this latter formulation, we propose a flux-upwind stabilization technique to deal with the advection-dominated case. The resulting scheme is conservative and satisfies a discrete...