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An unfitted finite element method using discontinuous Galerkin
Author(s) -
Bastian Peter,
Engwer Christian
Publication year - 2009
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.2631
Subject(s) - discontinuous galerkin method , discretization , finite element method , mathematics , galerkin method , grid , convergence (economics) , computation , scalar (mathematics) , domain (mathematical analysis) , polynomial , boundary value problem , mathematical optimization , mathematical analysis , algorithm , geometry , engineering , structural engineering , economics , economic growth
In this paper we present a new approach to simulations on complex‐shaped domains. The method is based on a discontinuous Galerkin (DG) method, using trial and test functions defined on a structured grid. Essential boundary conditions are imposed weakly via the DG formulation. This method offers a discretization where the number of unknowns is independent of the complexity of the domain. We will show numerical computations for an elliptic scalar model problem in ℝ 2 and ℝ 3 . Convergence rates for different polynomial degrees are studied. Copyright © 2009 John Wiley & Sons, Ltd.