Numerical studies of optimal grid construction

Chen, T.-F.; Fix, George J.; Yang, H. D.

doi:10.1002/(sici)1098-2426(199603)12:2<191::aid-num3>3.0.co;2-l

Cited by 7 publications

(3 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Moreover, extending these studies to problems in two or higher dimensions is important. Recently, based on equidistributing an appropriate grading function proposed in [4], optimal grids have been constructed when convection dominated problems in one and two dimensions are considered ( [5] and [6]). Such optimal grid construction technique with the nonlinear SOR for our model problem is currently under investigation and will be reported elsewhere.…”

Section: Numerical Resultsmentioning

confidence: 99%

Grid Refinement and Nonlinear Sor

Kannan

Chen

2001

Numerical Functional Analysis and Optimization

View full text Add to dashboard Cite

In this paper, finite difference and finite element methods are used with nonlinear SOR to solve the problems of minimizing strict convex functionals. The functionals are discretized by both methods and some numerical quadrature formula. The convergence of such discretization is guaranteed and will be discussed. As for the convergence of the iterative process, it is necessary to vary the relaxation parameter in each iterations. In addition, for the model catenoid problem, boundary grid refinements play an essential role in the proposed nonlinear SOR algorithm. Numerical results which illustrate the importance of the grid refinements will be presented.

show abstract

Section: Numerical Resultsmentioning

confidence: 99%

Grid Refinement and Nonlinear Sor

Kannan

Chen

2001

Numerical Functional Analysis and Optimization

View full text Add to dashboard Cite

show abstract

“…Based on the results in [3,4,7] and the nature of our model problem, it is necessary to consider also mesh refinement and smoothing. The algorithm in [7] is modified as follows: 1. Select initial grids, e.g., quasi-uniform grids.…”

Section: Numerical Algorithmmentioning

confidence: 99%

“…In [1], two-point boundary value problems were considered by Carey and Dinh and optimal grids were generated by equidistributing a grading function throughout the domain. Following their idea, based on finite element approximations, a mesh redistribution algorithm in two spatial dimensions was developed and applied to the convection dominated problems with great success [7]. Therefore, a mesh redistribution algorithm based on the weighted least-squares method will be employed in modeling transonic flow problems.…”

Section: Introductionmentioning

confidence: 99%

Adaptive least‐squares finite element approximations to transonic‐flow problems

Chang

Chen

2007

Proc Appl Math and Mech

View full text Add to dashboard Cite

This work concerns solutions of compressible potential flow problems based on weighted least-squares finite element approximations. The model problem considered is that of the potential flow past a circular cylinder. To capture the transonic flow region, an adaptive algorithm based on mesh redistribution with local mesh refinement and smoothing is developed for suitably weighted least-squares approximations. Numerical results for the model problem are given for the transonic case with shocks.

show abstract

Weighted least-squares approximationsto nonlinear hyperbolic equations

Chen

2004

Computers & Mathematics with Applications

View full text Add to dashboard Cite

Numerical studies of optimal grid construction

Cited by 7 publications

References 9 publications

Grid Refinement and Nonlinear Sor

Grid Refinement and Nonlinear Sor

Adaptive least‐squares finite element approximations to transonic‐flow problems

Weighted least-squares approximationsto nonlinear hyperbolic equations

Contact Info

Product

Resources

About