NDLI: A study on using hierarchical basis error estimates in anisotropic mesh adaptation for the finite element method

Content Provider	Springer Nature Link
Author	Kamenski, Lennard
Copyright Year	2011
Abstract	A common approach for generating an anisotropic mesh is the M-uniform mesh approach where an adaptive mesh is generated as a uniform one in the metric specified by a given tensor M. A key component is the determination of an appropriate metric, which is often based on some type of Hessian recovery. Recently, the use of a global hierarchical basis error estimator was proposed for the development of an anisotropic metric tensor for the adaptive finite element solution. This study discusses the use of this method for a selection of different applications. Numerical results show that the method performs well and is comparable with existing metric tensors based on Hessian recovery. Also, it can provide even better adaptation to the solution if applied to problems with gradient jumps and steep boundary layers. For the Poisson problem in a domain with a corner singularity, the new method provides meshes that are fully comparable to the theoretically optimal meshes.
Starting Page	451
Ending Page	460
Page Count	10
File Format	PDF
ISSN	01770667
Journal	Engineering with Computers
Volume Number	28
Issue Number	4
e-ISSN	14355663
Language	English
Publisher	Springer-Verlag
Publisher Date	2011-07-21
Publisher Place	London
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Mesh adaptation Anisotropic mesh Finite element A posteriori estimate Hierarchical basis Variational problem Anisotropic diffusion Mechanics Calculus of Variations and Optimal Control; Optimization Systems Theory, Control Math. Applications in Chemistry ApplicationMathematics/Computational Methods of Engineering Computer-Aided Engineering (CAD, CAE) and Design
Content Type	Text
Resource Type	Article
Subject	Engineering Computer Science Applications Modeling and Simulation Software

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