NA Seminar, Monika Eisenmann (Lund), "Randomized schemes for the approximation of nonlinear evolution equations"
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In this talk, we will focus on the numerical approximation of nonlinear, nonautonomous evolution equations with nonsmooth temporal coefficients. A common method for the approximation of the integral of an irregular function is a Monte Carlo type quadrature rule. We use a similar approach to approximate the solution of a nonautonomous evolution equation. First, we show how randomized point evaluations can be used to obtain error bounds when the data is merely integrable and the solution is Hölder continuous. A further randomization can be applied to generalize the regularity assumptions. After introducing a randomly shifted grid, it is possible to allow for a solution in a fractional Sobolev space and obtain error bounds of a possibly higher order.