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Journal of Scientific Computing
Published in: Journal of Scientific Computing 3/2018

02-11-2017

A Parallel Partition of Unity Scheme Based on Two-Grid Discretizations for the Navier–Stokes Problem

Authors: Guangzhi Du, Liyun Zuo

Published in: Journal of Scientific Computing | Issue 3/2018

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Abstract

A parallel partition of unity scheme based on two-grid discretizations is proposed and analyzed in this paper for the Navier–Stokes problem. A standard Galerkin finite element method on a relatively coarse grid is used to obtain the approximation of the lower frequency components and the higher frequency components are computed on fine grids by some local and parallel procedure. The motivation of the proposed parallel partition of unity scheme is based on the superposition principle. That is the original linear problem, which is a linear residual equation, can be equivalent to the sum of a series of simple problems of same type with free terms of small supports. Each simple problem is approximated by a local problem with homogeneous Dirichlet boundary condition. Optimal error estimates are obtained and some numerical tests are presented to support the theoretical results.
previous article A Multi-Level Mixed Element Method for the Eigenvalue Problem of Biharmonic Equation
next article A Lagrangian Scheme for the Solution of Nonlinear Diffusion Equations Using Moving Simplex Meshes

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Metadata
Title
A Parallel Partition of Unity Scheme Based on Two-Grid Discretizations for the Navier–Stokes Problem
Authors
Guangzhi Du
Liyun Zuo
Publication date
02-11-2017
Publisher
Springer US
Published in
Journal of Scientific Computing / Issue 3/2018
Print ISSN: 0885-7474
Electronic ISSN: 1573-7691
DOI
https://doi.org/10.1007/s10915-017-0593-6

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