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Discontinuous Galerkin framework for adaptive solution of parabolic problems
Author(s) -
Kulkarni Deepak V.,
Rovas Dimitrios V.,
Tortorelli Daniel A.
Publication year - 2006
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1828
Subject(s) - discretization , lagrange multiplier , discontinuous galerkin method , polygon mesh , a priori and a posteriori , isogeometric analysis , mathematics , scheme (mathematics) , mathematical optimization , finite element method , adaptive mesh refinement , galerkin method , component (thermodynamics) , constraint (computer aided design) , salient , computer science , mathematical analysis , geometry , computational science , structural engineering , engineering , philosophy , physics , epistemology , thermodynamics , artificial intelligence
Non‐conforming meshes are frequently employed in adaptive analyses and simulations of multi‐component systems. We develop a discontinuous Galerkin formulation for the discretization of parabolic problems that weakly enforces continuity across non‐conforming mesh interfaces. A benefit of the DG scheme is that it does not introduce constraint equations and their resulting Lagrange multiplier fields as done in mixed and mortar methods. The salient features of the formulation are highlighted through an a priori analysis. When coupled with a mesh refinement scheme the DG formulation is able to accommodate multiple hanging nodes per element edge and leads to an effective adaptive framework for the analysis of interface evolution problems. We demonstrate our approach by analysing the Stefan problem of solidification. Copyright © 2006 John Wiley & Sons, Ltd.