Convergence Analysis of Discretization Methods for Nonlinear First Kind Volterra Integral Equations.
Convergence analysis of finite difference schemes for semi-linear initial-value problems
Convergence analysis of piecewise continuous collocation methods for higher index integral algebraic equations of the Hessenberg type
In this paper, we deal with a system of integral algebraic equations of the Hessenberg type. Using a new index definition, the existence and uniqueness of a solution to this system are studied. The well-known piecewise continuous collocation methods are used to solve this system numerically, and the convergence properties of the perturbed piecewise continuous collocation methods are investigated to obtain the order of convergence for the given numerical methods. Finally, some numerical experiments...
Convergence analysis of preconditioned AOR iterative method for linear systems.
Convergence analysis of smoothing methods for optimal control of stationary variational inequalities with control constraints
In the article an optimal control problem subject to a stationary variational inequality is investigated. The optimal control problem is complemented with pointwise control constraints. The convergence of a smoothing scheme is analyzed. There, the variational inequality is replaced by a semilinear elliptic equation. It is shown that solutions of the regularized optimal control problem converge to solutions of the original one. Passing to the limit in the optimality system of the regularized problem...
Convergence Analysis of the General Gauss-Newton Algorithm.
Convergence analysis of the iterative methods for quasi-complementarity problems.
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 error estimates in finite volume schemes for general multidimensional scalar conservation laws. I. Explicite monotone schemes
Convergence and Nonlinear Stability of the Lagrange-Galerkin Method for the Navier-Stokes Equations.
Convergence and Order Reduction of Runge-Kutta Schemes Applied to Evolutionary Problems in Partial Differential 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 constant of the theta-method
The Euler methods are the most popular, simplest and widely used methods for the solution of the Cauchy problem for the first order ODE. The simplest and usual generalization of these methods are the so called theta-methods (notated also as -methods), which are, in fact, the convex linear combination of the two basic variants of the Euler methods, namely of the explicit Euler method (EEM) and of the implicit Euler method (IEM). This family of the methods is well-known and it is introduced almost...
Convergence and stability of a discontinuous Galerkin time-domain method for the 3D heterogeneous Maxwell equations on unstructured meshes
A Discontinuous Galerkin method is used for to the numerical solution of the time-domain Maxwell equations on unstructured meshes. The method relies on the choice of local basis functions, a centered mean approximation for the surface integrals and a second-order leap-frog scheme for advancing in time. The method is proved to be stable for cases with either metallic or absorbing boundary conditions, for a large class of basis functions. A discrete analog of the electromagnetic energy is conserved...
Convergence and stability of a discontinuous Galerkin time-domain method for the 3D heterogeneous Maxwell equations on unstructured meshes
A Discontinuous Galerkin method is used for to the numerical solution of the time-domain Maxwell equations on unstructured meshes. The method relies on the choice of local basis functions, a centered mean approximation for the surface integrals and a second-order leap-frog scheme for advancing in time. The method is proved to be stable for cases with either metallic or absorbing boundary conditions, for a large class of basis functions. A discrete analog of the electromagnetic energy is conserved...
Convergence and stability of difference scheme for an elliptic system of non-linear differential-functional equations with boundary conditions of Dirichlet type