Estimation of Discontinuous Coefficients in Parabolic Systems: Applications to Reservoir Simulation

We present spline-based techniques for estimating spatially varying parameters that appear in parabolic distributed systems (typical of those found in reservoir simulation problems). In particular, we discuss the problem of determining discontinuous coefficients, estimating both the functional shape and points of discontinuity for such parameters. In addition, our ideas may also be applied to problems with unknown initial conditions and unknown parameters appearing in terms representing external forces. Convergence results and a summary of numerical performance of the resulting algorithms are given.