Date of Award

2-22-2016

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Applied Science

First Advisor

Xiu Ye

Abstract

Parabolic equations have very broad applications in physics and engineering, such as heat diffusion and ocean acoustic propagation. Here we consider the 2D case with time dependent equations. Many numerical methods have been proposed to solve them, such as discontinuous Galerkin method, hybridized Galerkin method and so on. A weak Galerkin method is introduced by Dr. Wang and Dr. Ye by employing totally discontinuous functions in approximation space and an innovatively defined weak gradient operator which provide desirable flexibilities.In this thesis, we apply this method to solve parabolic equations. This method also has the energy conserva- tion property. Both continuous and discontinuous time weak Galerkin finite element methods are developed and analyzed, with optimal order estimates in H1 and L2 norms. Numerical experiments are provided.

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