Error estimation and adaptive meshing in strongly nonlinear dynamic problems

Multigrid Solution Strategies for Adaptive Meshing Problems

This paper discusses the issues which arise when combining multigrid strategies with adaptive meshing techniques for solving steady-state problems on unstructured meshes. A basic strategy is described, and demonstrated by solving several inviscid and viscous ow cases. Potential ine ciencies in this basic strategy are exposed, and various alternate approaches are discussed, some of which are dem...

Adaptive Boundary Elements and Error Estimation for Elastic Problems

In traditional thinking, when the elastic problems are solved, we need to repeatedly plot element grids and analyze computing results according to diverse precision requirement. Against the malpractice exists in the above process, a new method of error estimation was suggested on H-R adaptive boundary element method in this paper. Based on the discrete meshes that are generated for the process ...

Goal-oriented error estimation for fast approximations of nonlinear problems

Error estimation in nonlinear optimization

Methods are developed and analyzed for estimating the distance to a local minimizer of a nonlinear programming problem. One estimate, based on the solution of a constrained convex quadratic program, can be used when strict complementary slackness and the second-order sufficient optimality conditions hold. A second estimate, based on the solution of an unconstrained nonconvex, nonsmooth optimiza...

An adaptive Dynamic Relaxation method for solving nonlinear finite element problems. Application to brain shift estimation.

Dynamic Relaxation is an explicit method that can be used for computing the steady state solution for a discretised continuum mechanics problem. The convergence speed of the method depends on the accurate estimation of the parameters involved, which is especially difficult for nonlinear problems. In this paper we propose a completely adaptive Dynamic Relaxation method in which the parameters ar...