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Higher order discretisation of initial-boundary value problems for mixed systems

by R. Bodenmann and H. J. Schroll

(Report number 1996-05)

Abstract
An initial-boundary value problem for a system of nonlinear partial differential equations, which consists of a hyperbolic and a parabolic part, is taken into consideration. Spacial derivatives are discretised by third order consistent difference operators, which are constructed such that a summation by parts formula holds. Therefore the space discretisation is energy bounded and algebraically stable implicit Runge-Kutta methods can be applied to integrate in time. Boundary layers arising from the artificial boundary conditions are analysed and nonlinear convergence is proved.

Keywords: Higher order difference method, initial-boundary value problem, boundary layer, nonlinear hyperbolic-parabolic system, local stability, convergence.

@Techreport{BS96_188,
  author = {R. Bodenmann and H. J. Schroll},
  title = {Higher order discretisation of initial-boundary value problems for mixed systems},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {1996-05},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports1996/1996-05.pdf },
  year = {1996}
}

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