@article{ Lang2003,
  abstract = {In this paper, we consider the numerical solution of time-dependent PDEs using a finite element method based upon rh-adaptivity. An adaptive horizontal method of lines strategy equipped with a posteriori error estimates to control the discretization through variable time steps and spatial grid adaptations is used. Our approach combines an r-refinement method based upon solving so-called moving mesh PDEs with h-refinement. Numerical results are presented to demonstrate the capabilities and benefits of combining mesh movement and local refinement. © 2003 IMACS. Published by Elsevier Science B.V. All rights reserved.},
  author = {Lang, Jens and Cao, Weiming and Huang, Weizhang and Russell, Robert D.},
  doi = {10.1016/S0168-9274(03)00013-8},
  isbn = {0168-9274},
  issn = {01689274},
  journal = {Applied Numerical Mathematics},
  keywords = {A posteriori error estimates,Local refinement,Moving mesh methods,Multilevel finite elements,Nonlinear time-dependent PDEs,Rosenbrock methods},
  pages = {75--94},
  title = {{A two-dimensional moving finite element method with local refinement based on a posteriori error estimates}},
  volume = {46},
  year = {2003}
}

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