Blar i forfatter Artikler, rapporter og annet (automasjon og prosessteknologi) "Grunert, Katrin"

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    • A Convergent Numerical Algorithm for α-Dissipative Solutions of the Hunter–Saxton Equation 

      Christiansen, Thomas; Grunert, Katrin; Nordli, Anders Samuelsen; Solem, Susanne (Journal article; Tidsskriftartikkel; Peer reviewed, 2024-03-02)
      A convergent numerical method for α -dissipative solutions of the Hunter–Saxton equation is derived. The method is based on applying a tailor-made projection operator to the initial data, and then solving exactly using the generalized method of characteristics. The projection step is the only step that introduces any approximation error. It is therefore crucial that its design ensures not only a ...

    • Numerical conservative solutions of the Hunter–-Saxton equation 

      Grunert, Katrin; Nordli, Anders Samuelsen; Solem, Susanne (Journal article; Tidsskriftartikkel; Peer reviewed, 2021-01-21)
      In the article a convergent numerical method for conservative solutions of the Hunter–Saxton equation is derived. The method is based on piecewise linear projections, followed by evolution along characteristics where the time step is chosen in order to prevent wave breaking. Convergence is obtained when the time step is proportional to the square root of the spatial step size, which is a milder ...