An Automatic Adaptive Re nement and Dere nement Method for D Elliptic Problems
نویسندگان
چکیده
We present the theory and implementation for a new automatic adaptive h re nement and dere nement method for two and three dimensional elliptic problems An exact lower error bound for dere nement is obtained theoretically in terms of the nite element solution complementing the various known upper error bounds for re nement These error bounds are used to determine where to insert and or remove mesh elements To implement the method we utilize an adaptive two and three dimensional Delaunay tessellation that preserves the Delaunay properties while locally adding points to or deleting points from the previous Delaunay mesh We provide computational examples for two and three dimensional elliptic problems on unstructured grids
منابع مشابه
An Automatic Adaptive Reenement and Dereenement Method for 3d Elliptic Problems
We present the theory and implementation for a new automatic adaptive h-re nement and -dere nement method for twoand three-dimensional elliptic problems. An exact lower error bound for dere nement is obtained theoretically in terms of the nite element solution, complementing the various known upper error bounds for re nement. These error bounds are used to determine where to insert and/or remov...
متن کاملPii: S0965-9978(98)00069-6
A node-based data structure is developed for use in either two-dimensional (2-D) or three-dimensional (3-D) ®nite element method (FEM) problems. This grid uses quadrilateral (2-D) or hexahedral (3-D) elements and is dynamically adaptive according to the 1-irregular requirement for re®nement±dere®nement. Implemented in C 1 1 , the grid consists of node objects linked with pointers to neighboring...
متن کاملAdaptive Mesh Re nement and Multilevel Iteration for Flow inPorous
An adaptive local mesh re nement algorithm originally developed for unsteady gas dynamics by Berger [12, 14] is extended to incompressible ow in porous media. Multilevel iteration and domain decomposition methods are introduced to accommodate the elliptic/parabolic aspects of the ow equations. The algorithm is applied to a two-phase polymer ooding model consisting of a system of nonlinear hyper...
متن کاملA Comparison of Three Adaptive Finite Element Re nement Techniques for Incompressible Navier-Stokes Equations Using a CBS Scheme
The numerical solution of incompressible Navier-Stokes equations for ows involving complex geometries is greatly a ected by mesh resolution. In these ows, some regions may need ner mesh than others. Adaptive Mesh Re nement (AMR) techniques enable the mesh to be locally re ned, based on error distribution in the previous analysis. In this paper, three adaptive re nement methods, namely, Supercon...
متن کاملAnisotropic Patch-Based Adaptive Mesh Re nement for Finite-Volume Method
We propose an anisotropic, patch-based adaptive mesh re nement algorithm for the nite-volume method solving partial di erential equations on Cartesian and mapped grids. For large ow gradients, such as shock waves and ame fronts, that are aligned with one grid direction, anisotropic re nement can provide a similar reduction in error using much less grid cells compared to isotropic re nement. To ...
متن کامل