Stochastic Partial Differential Equationswire

Seminar zum Wissenschaftlichen Rechnen - Wintersemester 2010/2011

Stochastic Partial Differential Equations

During the last years Stochastic Partial Differential Equations SPDEs become very popular for modeling uncertainties in physical and engineering applications. The philosophy is that modern numerical methods are able to produce very high accuracy of the solution, whereas the input data (parameters, coefficients, the right-hand side, initial and boundary conditions) are often contain measurement errors or/and are not completely known. It can, for instance, be known not the concrete value of a parameter, but only its cumulative distribution function (Gaussian, uniform etc). The solution in this case will be also not a function, but some distribution and the values of interest will be the mean value, the variance, exceedance probabilities and other functionals of the solution. To make simulation models more accurate the engineers would like to know how uncertainties in the input data propagate to the solution. In the frame of the seminar work we offer to students to make overview of available techniques for identification, classification and quantification of uncertainties. The institute has already a rich library for solving SPDEs SGLIB (developed by Elmar Zander).

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