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Journal of Computational Physics 172, 609639 (2001) doi:10.1006/jcph.2001.6844, available online at http://www.idealibrary.com on
 

Summary: Journal of Computational Physics 172, 609639 (2001)
doi:10.1006/jcph.2001.6844, available online at http://www.idealibrary.com on
An Efficient Dynamically Adaptive Mesh
for Potentially Singular Solutions
Hector D. Ceniceros and Thomas Y. Hou
Department of Mathematics, University of California Santa Barbara, Santa Barbara, California 93106; and
Applied Mathematics, California Institute of Technology, Pasadena, California 91125
E-mail: hdc@math.ucsb.edu; hou@ama.caltech.edu
Received May 2, 2000; revised May 29, 2001
We develop an efficient dynamically adaptive mesh generator for time-dependent
problems in two or more dimensions. The mesh generator is motivated by the vari-
ational approach and is based on solving a new set of nonlinear elliptic PDEs for
the mesh map. When coupled to a physical problem, the mesh map evolves with the
underlying solution and maintains high adaptivity as the solution develops compli-
cated structures and even singular behavior. The overall mesh strategy is simple to
implement, avoids interpolation, and can be easily incorporated into a broad range
of applications. The efficacy of the mesh is first demonstrated by two examples of
blowing-up solutions to the 2-D semilinear heat equation. These examples show that
the mesh can follow with high adaptivity a finite-time singularity process. The focus
of applications presented here is however the baroclinic generation of vorticity in

  

Source: Akhmedov, Azer - Department of Mathematics, University of California at Santa Barbara
Hou, Thomas Yizhao - Applied and Computational Mathematics Department, California Institute of Technology

 

Collections: Mathematics