Kuznetsov, Yuri2017-04-302017-04-30May 20152015-05May 2015http://hdl.handle.net/10657/1743In this dissertation, we consider a new mixed finite element discretization, its error estimation, monotonicity and the approaches to implement local refinement. We also do some numerical experiments to verify error estimates and to see the effect of distorted faces. In the first part, we introduce a discontinuous Galerkin method based on piece-wise constant fluxes, we elaborate its construction and discretization on triangular meshes. We then consider the monotonicity of this method, compare it with classical RT0 method and extend to KR methods. Finally, error estimation is investigated. In the second part, we start from reviewing traditional approaches to implement local refinement for the new mixed finite element method. Because of disappearance of monotonicity, we then try to find an alternative way to do local refinement to keep monotonicity. In the third part, we implement this method on a specially constructed prismatic grid. Numerical results are provided. We then verify the error estimates from the numerical results.application/pdfengThe author of this work is the copyright owner. UH Libraries and the Texas Digital Library have their permission to store and provide access to this work. Further transmission, reproduction, or presentation of this work is prohibited except with permission of the author(s).Mixed finite element methodsPiece-wise constant fluxesMonotonicityError estimationsLocal refinement2017-04-30Thesisborn digital