Convergence of Finite-difference Schemes for Poisson's Equation With Boundary Condition of the Third Kind
Convergence of some adaptive FEM-BEM coupling for elliptic but possibly nonlinear interface problems
We consider the symmetric FEM-BEM coupling for the numerical solution of a (nonlinear) interface problem for the 2D Laplacian. We introduce some new a posteriori error estimators based on the (h − h/2)-error estimation strategy. In particular, these include the approximation error for the boundary data, which allows to work with discrete boundary integral operators only. Using the concept of estimator reduction, we prove that the proposed adaptive...
Convergence of some adaptive FEM-BEM coupling for elliptic but possibly nonlinear interface problems
We consider the symmetric FEM-BEM coupling for the numerical solution of a (nonlinear) interface problem for the 2D Laplacian. We introduce some new a posteriori error estimators based on the (h − h/2)-error estimation strategy. In particular, these include the approximation error for the boundary data, which allows to work with discrete boundary integral operators only. Using the concept of estimator reduction, we prove that the proposed adaptive...
Convergence rate of a finite volume scheme for a two dimensional convection-diffusion problem
Convergence rate of a finite volume scheme for a two dimensional convection-diffusion problem
In this paper, a class of cell centered finite volume schemes, on general unstructured meshes, for a linear convection-diffusion problem, is studied. The convection and the diffusion are respectively approximated by means of an upwind scheme and the so called diamond cell method [4]. Our main result is an error estimate of order h, assuming only the W2,p (for p>2) regularity of the continuous solution, on a mesh of quadrangles. The proof is based on an extension of the ideas developed in...
Convergence rate of a finite volume scheme for the linear convection-diffusion equation on locally refined meshes
Convergence rate of a finite volume scheme for the linear convection-diffusion equation on locally refined meshes
We study a finite volume method, used to approximate the solution of the linear two dimensional convection diffusion equation, with mixed Dirichlet and Neumann boundary conditions, on Cartesian meshes refined by an automatic technique (which leads to meshes with hanging nodes). We propose an analysis through a discrete variational approach, in a discrete H1 finite volume space. We actually prove the convergence of the scheme in a discrete H1 norm, with an error estimate of order O(h) (on meshes...
Covolume techniques for anisotropic media.
Der Einfluß von Randsingularitäten beim Ritzschen Verfahren. - Solution Effects of the Ritz Method.
Development of local, global, and trace estimates for the solutions of elliptic equations.
Die maximale Konsistenzordnung von Differenzenapproximationen nichtnegativer Art.
Difference inequalities of the elliptic type
Difference method for an elliptic system of nonlinear differential-functional equations.
Difference scheme for the Vlasov-Manev system.
Differenzenverfahren zur Berechnung periodischer Lösungen von hyperbolischen Differentialgleichungen.
Diffusion with dissolution and precipitation in a porous medium: Mathematical analysis and numerical approximation of a simplified model
Modeling the kinetics of a precipitation dissolution reaction occurring in a porous medium where diffusion also takes place leads to a system of two parabolic equations and one ordinary differential equation coupled with a stiff reaction term. This system is discretized by a finite volume scheme which is suitable for the approximation of the discontinuous reaction term of unknown sign. Discrete solutions are shown to exist and converge towards a weak solution of the continuous problem. Uniqueness...
Dirichlet-Neumann alternating algorithm for an exterior anisotropic quasilinear elliptic problem
In this paper, by the Kirchhoff transformation, a Dirichlet-Neumann (D-N) alternating algorithm which is a non-overlapping domain decomposition method based on natural boundary reduction is discussed for solving exterior anisotropic quasilinear problems with circular artificial boundary. By the principle of the natural boundary reduction, we obtain natural integral equation for the anisotropic quasilinear problems on circular artificial boundaries and construct the algorithm and analyze its convergence....
Discrete approximation of the solution of the Dirichlet problem by discrete means.
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.