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Optimal space-time adaptive wavelet methods for degenerate parabolic PDEs

by O. Reichmann

(Report number 2011-03)

Abstract
We analyze parabolic PDEs with certain type of weakly singular or degenerate time-dependent coefficients and prove existence and uniqueness of weak solutions in an appropriate sense. A localization of the PDEs to a bounded spatial domain is justified. For the numerical solution a space-time wavelet discretization is employed. An optimality result for the iterative solution of the arising systems can be obtained. Applications to fractional Brownian motion models in option pricing are presented.

Keywords: Degenerate parabolic differential equations, wavelets, adaptivity, optimal computational complexity, best N-term approximation, fractional Brownian Motion

@Techreport{R11_146,
  author = {O. Reichmann},
  title = {Optimal space-time adaptive wavelet methods for degenerate parabolic PDEs},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2011-03},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2011/2011-03.pdf },
  year = {2011}
}

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