A note on the unique solvability of a class of nonlinear equations.
A parameter choice for Tikhonov regularization for solving nonlinear inverse problems leading to optimal convergence rates
We give a derivation of an a-posteriori strategy for choosing the regularization parameter in Tikhonov regularization for solving nonlinear ill-posed problems, which leads to optimal convergence rates. This strategy requires a special stability estimate for the regularized solutions. A new proof fot this stability estimate is given.
A penalty approach for a box constrained variational inequality problem
We propose a penalty approach for a box constrained variational inequality problem . This problem is replaced by a sequence of nonlinear equations containing a penalty term. We show that if the penalty parameter tends to infinity, the solution of this sequence converges to that of when the function involved is continuous and strongly monotone and the box contains the origin. We develop the algorithmic aspect with theoretical arguments properly established. The numerical results tested on...
A Perturbed Iterative Method for a General Class of Variational Inequalities
The generalized Wiener-Hopf equation and the approximation methods are used to propose a perturbed iterative method to compute the solutions of a general class of nonlinear variational inequalities.
A posteriori error analysis of the fully discretized time-dependent Stokes equations
The time-dependent Stokes equations in two- or three-dimensional bounded domains are discretized by the backward Euler scheme in time and finite elements in space. The error of this discretization is bounded globally from above and locally from below by the sum of two types of computable error indicators, the first one being linked to the time discretization and the second one to the space discretization.
A posteriori error analysis of the fully discretized time-dependent Stokes equations
The time-dependent Stokes equations in two- or three-dimensional bounded domains are discretized by the backward Euler scheme in time and finite elements in space. The error of this discretization is bounded globally from above and locally from below by the sum of two types of computable error indicators, the first one being linked to the time discretization and the second one to the space discretization.
A posteriori estimations of approximate solutions for some types of boundary value problems
A Predictor-Corrector Technique for Constrained Least-Squares Regularization.
A principle of dehomogenization for eigenvalue problems (Preliminary communication)
A priori-Schranken für diskrete Lösungen monotoner Operatorgleichungen und Anwendungen.
A quasi-Newton method for solving fixed point problems in Hilbert spaces.
A reduction method for approximate solving large elliptic systems
A refined Newton’s mesh independence principle for a class of optimal shape design problems
Shape optimization is described by finding the geometry of a structure which is optimal in the sense of a minimized cost function with respect to certain constraints. A Newton’s mesh independence principle was very efficiently used to solve a certain class of optimal design problems in [6]. Here motivated by optimization considerations we show that under the same computational cost an even finer mesh independence principle can be given.
A Regularized Continuous Projection-Gradient Method of the Fourth Order
A remark on solving large systems of equations in function spaces
In order to save CPU-time in solving large systems of equations in function spaces we decompose the large system in subsystems and solve the subsystems by an appropriate method. We give a sufficient condition for the convergence of the corresponding procedure and apply the approach to differential algebraic systems.
A SOR Acceleration of Self-Adjoint and m-Accretive Splitting Iterative Solver for 2-D Neutron Transport Equation
We present an iterative method based on an infinite dimensional adaptation of the successive overrelaxation (SOR) algorithm for solving the 2-D neutron transport equation. In a wide range of application, the neutron transport operator admits a Self-Adjoint and m-Accretive Splitting (SAS). This splitting leads to an ADI-like iterative method which converges unconditionally and is equivalent to a fixed point problem where the operator is a 2 by 2 matrix...
A (...)-stable approximations of abstract Cauchy problems.
A study of Galerkin method for the heat convection equations
The paper investigates the Galerkin method for an initial boundary value problem for heat convection equations. New error estimates for the approximate solutions and their derivatives in strong norm are obtained.
A unified analysis of elliptic problems with various boundary conditions and their approximation
We design an abstract setting for the approximation in Banach spaces of operators acting in duality. A typical example are the gradient and divergence operators in Lebesgue-Sobolev spaces on a bounded domain. We apply this abstract setting to the numerical approximation of Leray-Lions type problems, which include in particular linear diffusion. The main interest of the abstract setting is to provide a unified convergence analysis that simultaneously covers (i) all usual boundary conditions, (ii)...
A Unified Approach for Constructing Fast Two-Step Newton-like Methods.