Finite Volume Element Methods for Flow Problems in Porous Media

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Chou0074259 The investigator studies the convergence, stability, and superconvergence of finite volume element type methods, and implements algorithms in software. A general framework is developed for mixed control volume methods on irregular grids. Furthermore, nonlinear covolume methods applied to parabolic differential and integro-differential equations are studied. Fluid flow problems such as chemical or radioactive contaminant transport in subsurface reservoir flow, displacement of oil in the oil recovery process, and bioremediation of aquifers, are complex and difficult to simulate computationally. Yet they are important for the environment and for managing energy resources. The investigator develops, analyzes, and implements a class of computational methods called finite volume element methods that seem to have some advantages over other methods but that have not been rigorously analyzed yet. The analysis undertaken in the project should establish a firm theoretical footing for the methods. This is important for the reliability and validity of computations performed with the methods.