An Adaptive H-refinement Finite Element Method for Reaction-diffusion Systems in Three Space Dimensions
نویسنده
چکیده
I describe an adaptive h-reenement method for solving reaction-diiusion systems in three space dimensions on hexahedral grids. These grids typically have irregular (hanging) nodes. Solutions are calculated using Galerkin's method with a piecewise trilinear basis in space and a BDF code in time. New a posteriori error indicators based on interpolation error estimates for irregular grids are used to control reenement and coarsening. Computational results demonstrate the eeectiveness of the adaptive method on reaction-diiusion equations.
منابع مشابه
Effects of Basis Selection and H-refinement on Error Estimator Reliability and Solution Efficiency for High-order Methods in Three Space Dimensions
Designing effective high-order adaptive methods for solving stationary reaction-diffusion equations in three dimensions requires the selection of a finite element basis, a posteriori error estimator and refinement strategy. Estimator accuracy may depend on the basis chosen, which in turn, may lead to unreliability or inefficiency via underor over-refinement, respectively. The basis may also hav...
متن کاملAn Adaptive H-refinement Finite Element Method for Parabolic Differential Systems in Three Space Dimensions
I describe an adaptive h-reenement method for solving systems of parabolic partial diierential equations in three space dimensions on hexahedral grids. These grids typically have irregular (hanging) nodes. Solutions are calculated using Galerkin's method with a piecewise trilinear basis in space and a BDF code in time. New a posteriori error indicators based on interpolation error estimates for...
متن کاملComparison of different numerical methods for calculating stress intensity factors in analysis of fractured structures
In this research, an efficient Galerkin Finite Volume Method (GFVM) along with the h–refinement adaptive process and post–processing error estimation analysis is presented for fracture analysis. The adaptive strategy is used to produce more accurate solution with the least computational cost. To investigate the accuracy and efficiency of the developed model, the GFVM is compared with two versio...
متن کاملConvergence of an adaptive hp finite element strategy in higher space-dimensions
We show convergence in the energy norm for an automatic hp-adaptive refinement strategy for finite elements on the elliptic boundary value problem. The result is a generalization of a marking strategy, which was proposed in one space-dimension, to problems in twoand three-dimensional spaces.
متن کاملAdaptive Finite Element Method Assisted by Stochastic Simulation of Chemical Systems
Stochastic models of chemical systems are often analysed by solving the corresponding Fokker-Planck equation which is a drift-diffusion partial differential equation for the probability distribution function. Efficient numerical solution of the Fokker-Planck equation requires adaptive mesh refinements. In this paper, we present a mesh refinement approach which makes use of a stochastic simulati...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2007