Non-overlapping domain decomposition parallel algorithms for convection-diffusion problems

Domain decomposition has many benefits that, with the plethora of fast and cheap computers, allow for large problems to be solved in parallel at speeds that were previously unattainable. This dissertation builds on known algorithms, extends and expands methods of solving the general convection-diffusion equation with non-overlapping domain decomposition by numerical methods through modifying the designed interface computation. Maximum principles are employed for stability and error estimates of the algorithms and several numerical studies of performance are developed.