Convergence Properties of the Runge-Kutta-Chebyshev Method.
Convergence rate estimate for a domain decomposition method.
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...
Convergence rates for regularization with sparsity constraints.
Convergence rates for the approximations of the solutions to algebraic Riccati Equations with unbounded coefficients: case of analytic semigroups.
Convergence rates for the full gaussian rough paths
Under the key assumption of finite -variation, , of the covariance of the underlying Gaussian process, sharp a.s. convergence rates for approximations of Gaussian rough paths are established. When applied to Brownian resp. fractional Brownian motion (fBM), resp. , we recover and extend the respective results of (Trans. Amer. Math. Soc.361 (2009) 2689–2718) and (Ann. Inst. Henri Poincasé Probab. Stat.48(2012) 518–550). In particular, we establish an a.s. rate , any , for Wong–Zakai and Milstein-type...
Convergence rates of iterated Tikhonov regularized solutions of nonlinear Ill-posed problems.
Convergence Rates of the POD–Greedy Method
Iterative approximation algorithms are successfully applied in parametric approximation tasks. In particular, reduced basis methods make use of the so-called Greedy algorithm for approximating solution sets of parametrized partial differential equations. Recently, a priori convergence rate statements for this algorithm have been given (Buffa et al. 2009, Binev et al. 2010). The goal of the current study is the extension to time-dependent problems, which are typically approximated using the POD–Greedy...
Convergence Results for an Accelerated Nonlinear Cimmino Algorithm.
Convergence results of the fictitious domain method for a mixed formulation of the wave equation with a Neumann boundary condition
The problem of modeling acoustic waves scattered by an object with Neumann boundary condition is considered. The boundary condition is taken into account by means of the fictitious domain method, yielding a first order in time mixed variational formulation for the problem. The resulting system is discretized with two families of mixed finite elements that are compatible with mass lumping. We present numerical results illustrating that the Neumann boundary condition on the object is not always correctly...
Convergence results of the fictitious domain method for a mixed formulation of the wave equation with a Neumann boundary condition
The problem of modeling acoustic waves scattered by an object with Neumann boundary condition is considered. The boundary condition is taken into account by means of the fictitious domain method, yielding a first order in time mixed variational formulation for the problem. The resulting system is discretized with two families of mixed finite elements that are compatible with mass lumping. We present numerical results illustrating that the Neumann boundary condition on the object is not always...
Convergence theorems for Newton-like methods using data from a set or a single point and outer inverses.
Convergence theory for inexact inverse iteration applied to the generalised nonsymmetric eigenproblem.
Convergence theory for the exact interpolation scheme with approximation vector as the first column of the prolongator and Rayleigh quotient iteration nonlinear smoother
We extend the analysis of the recently proposed nonlinear EIS scheme applied to the partial eigenvalue problem. We address the case where the Rayleigh quotient iteration is used as the smoother on the fine-level. Unlike in our previous theoretical results, where the smoother given by the linear inverse power method is assumed, we prove nonlinear speed-up when the approximation becomes close to the exact solution. The speed-up is cubic. Unlike existent convergence estimates for the Rayleigh quotient...
Convergence Theory of Extrapolated Iterative Methods for a Certain Class of Non-Symmetric Linear Systems.
Convergence to compact sets of inexact orbits of nonexpansive mappings in Banach and metric spaces.
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.