Mathematical Sciences: Numerical Solution of Partial Differential Equations

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This research involves the numerical solution of a collection of problems arising in geophysics, petroleum engineering, and biological contexts. Finite element procedures and homogenization will be used to continue work on flow of a compressible fluid in a fractured reservoir. Model problems simulating the contraction of a viscoelastic muscle will be studied numerically by developing methods for the numerical solution of the appropriate nonlinear time-dependent partial differential and integro-differential equations and systems.