A pre-processing moving mesh method for discontinuous Galerkin approximations of advection-diffusion-reaction problems
Paola F. Antonietti 1, Paul Houston 21 Dipartimento di Matematica, Università degli Studi di Pavia, Via Ferrata 1, 27100 Pavia, Italy
2 School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, UK
Received by the editors December 11, 2007
We propose a pre-processing mesh re-distribution algorithm based upon harmonic maps employed in conjunction with discontinuous Galerkin approximations of advection-diffusion-reaction problems. Extensive two-dimensional numerical experiments with different choices of monitor functions, including monitor functions derived from goal-oriented a posteriori error indicators are presented. The examples presented clearly demonstrate the capabilities and the benefits of combining our pre-processing mesh movement algorithm with both uniform, as well as, adaptive isotropic and anisotropic mesh refinement.
AMS subject classifications: 65N30
Key words: discontinuous Galerkin methods; advection-diffusion problems; adaptivity
Email: email@example.com (P. F. Antonietti), Paul.Houston@nottingham.ac.uk (P. Houston)