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This course builds upon MATH 5520 by providing introductions to mixed, hybrid and discontinuous-Galerkin (DG) finite element methods. Flow in porous media will serve as an application to motivate canonical mathematical models. We develop various discretizations, stability and convergence properties, algebraic systems and comparisons of methods. The focus will remain on elliptic problems, with some brief coverage of (stationary) hyperbolic problems.Homework: About four written homework assignments, which will be posted below over time.