Fu, Guosheng2016-09-192016-09-192016-05https://hdl.handle.net/11299/182270University of Minnesota Ph.D. dissertation. May 2016. Major: Mathematics. Advisor: Bernardo Cockburn. 1 computer file (PDF); xi, 260 pages.In this thesis, we develop the concept of an M-decomposition as an effective tool for devising high-order accurate hybridizable discontinuous Galerkin methods and hybridized mixed methods that superconverge on unstructured meshes of shape-regular polyhedral elements for three linear elliptic partial differential equations, namely, the (steady-state) diffusion equation, the equations for linear elasticity, and the equations for incompressible Stokes flow.endiscontinuous GalerkinhybridizationM-decompositionmixed methodsThesis or Dissertation