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Convergence rates of finite difference schemes for the wave equation with rough coeffiicients

by S. Mishra and N. Risebro and F. Weber

(Report number 2013-42)

Abstract
The propagation of acoustic waves in a rough heterogeneous medium is modeled using the linear wave equation with a variable but merely Hölder continuous coefficient. We design robust finite difference discretizations that are shown to converge to the weak solution. We rigorously determine the rate of convergence of these discretizations by an \(L^2\) variant of the Kruzkhov doubling of variables technique. Numerical experiments illustrating these rates of convergence are also presented.

Keywords: Wave equation, finite difference schemes, rough coefficients

@Techreport{MRW13_540,
  author = {S. Mishra and N. Risebro and F. Weber},
  title = {Convergence rates of finite difference schemes for the wave equation with rough coeffiicients},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2013-42},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2013/2013-42.pdf },
  year = {2013}
}

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