Abstract
This chapter presents a new class of flexible Galerkin methods that allow for nonuniform continuity levels across element boundaries. The flexible Galerkin (FG) finite element method for solving partial differential equations is a hybrid of the standard continuous Galerkin (CG) method and the discontinuous Galerkin (DG) method. A major overhead associated with DG methods comes from the large number of degrees of freedom because entities on inter-element boundaries are not shared. To obtain an efficient hp adaptive flexible Galerkin method, the representation is hierarchical with elements having pointers to their bounding edges which, in turn, have pointers to their bounding vertices.
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