Mesh-Hardened Finite Element Analysis Through a Generalized Moving Least-Squares Approximation of Variational Problems
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In most finite element methods the mesh is used to both represent the domain and to define the finite element basis. As a result the quality of such methods is tied to the quality of the mesh and may suffer when the latter deteriorates. This paper formulates an alternative approach, which separates the discretization of the domain, i.e., the meshing, from the discretization of the PDE. The latter is accomplished by extending the Generalized Moving Least-Squares (GMLS) regression technique to approximation of bilinear forms and using the mesh only for the integration of the GMLS polynomial basis. Our approach yields a non-conforming discretization of the weak equations that can be handled by standard discontinuous Galerkin or interior penalty terms.
KeywordsGalerkin methods Generalized Moving Least Squares Nonconforming finite elements
This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research under Award Number DE-SC-0000230927, and the Laboratory Directed Research and Development program at Sandia National Laboratories.
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