Convergence analysis for an exponentially fitted finite volume method
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 analysis of a locally stabilized collocated finite volume scheme for incompressible flows
We present and analyse in this paper a novel cell-centered collocated finite volume scheme for incompressible flows. Its definition involves a partition of the set of control volumes; each element of this partition is called a cluster and consists in a few neighbouring control volumes. Under a simple geometrical assumption for the clusters, we obtain that the pair of discrete spaces associating the classical cell-centered approximation for the velocities and cluster-wide constant pressures is inf-sup...
Convergence analysis of a nonconforming finite element method solving a plate with ribs
Convergence analysis of the lowest order weakly penalized adaptive discontinuous Galerkin methods
In this article, we prove convergence of the weakly penalized adaptive discontinuous Galerkin methods. Unlike other works, we derive the contraction property for various discontinuous Galerkin methods only assuming the stabilizing parameters are large enough to stabilize the method. A central idea in the analysis is to construct an auxiliary solution from the discontinuous Galerkin solution by a simple post processing. Based on the auxiliary solution, we define the adaptive algorithm which guides...
Convergence analysis of the rotated element on anisotropic rectangular meshes.
Convergence and Comparison Analysis of Some Numerical Schwarz Methods.
Convergence and Nonlinear Stability of the Lagrange-Galerkin Method for the Navier-Stokes Equations.
Convergence and quasi-optimal complexity of a simple adaptive finite element method
We prove convergence and quasi-optimal complexity of an adaptive finite element algorithm on triangular meshes with standard mesh refinement. Our algorithm is based on an adaptive marking strategy. In each iteration, a simple edge estimator is compared to an oscillation term and the marking of cells for refinement is done according to the dominant contribution only. In addition, we introduce an adaptive stopping criterion for iterative solution which compares an estimator for the iteration error...
Convergence and regularization results for optimal control problems with sparsity functional
Optimization problems with convex but non-smooth cost functional subject to an elliptic partial differential equation are considered. The non-smoothness arises from a L1-norm in the objective functional. The problem is regularized to permit the use of the semi-smooth Newton method. Error estimates with respect to the regularization parameter are provided. Moreover, finite element approximations are studied. A-priori as well as a-posteriori error estimates are developed and confirmed by numerical...
Convergence and regularization results for optimal control problems with sparsity functional
Optimization problems with convex but non-smooth cost functional subject to an elliptic partial differential equation are considered. The non-smoothness arises from a L1-norm in the objective functional. The problem is regularized to permit the use of the semi-smooth Newton method. Error estimates with respect to the regularization parameter are provided. Moreover, finite element approximations are studied. A-priori as well as a-posteriori error estimates are developed and confirmed by numerical...
Convergence and stability of difference scheme for an elliptic system of non-linear differential-functional equations with boundary conditions of Dirichlet type
Convergence conditions for Secant-type methods
We provide new sufficient convergence conditions for the convergence of the secant-type methods to a locally unique solution of a nonlinear equation in a Banach space. Our new idea uses recurrent functions, and Lipschitz-type and center-Lipschitz-type instead of just Lipschitz-type conditions on the divided difference of the operator involved. It turns out that this way our error bounds are more precise than earlier ones and under our convergence hypotheses we can cover cases where earlier conditions...
Convergence Near Plane Boundaries of Some Elliptic Difference Schemes.
Convergence of a dual finite element method in
Convergence of a Finite Difference Method for the Third BVP for Poisson's Equation
Convergence of a finite difference scheme for the third boundary-value problem.
Convergence of a finite element discretization of the Navier-Stokes equations in vorticity and stream function formulation
Convergence of a finite element discretization of the Navier-Stokes equations in vorticity and stream function formulation
The standard discretization of the Stokes and Navier–Stokes equations in vorticity and stream function formulation by affine finite elements is known for its bad convergence. We present here a modified discretization, we prove that the convergence is improved and we establish a priori error estimates.
Convergence of a finite element method based on the dual variational formulation