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math.NA2020★ 5 cited
A numerical study of variational discretizations of the Camassa-Holm equation
Sondre Tesdal Galtung, Katrin Grunert
We present two semidiscretizations of the Camassa-Holm equation in periodic domains based on variational formulations and energy conservation. The first is a periodic version of an…
math.NA2016★ 9 cited
A Convergent Crank-Nicolson Galerkin Scheme for the Benjamin-Ono Equation
Sondre Tesdal Galtung
In this paper we prove the convergence of a Crank-Nicolson type Galerkin finite element scheme for the initial value problem associated to the Benjamin-Ono equation. The proof is b…
math.NA2016
Convergence Rates of a Fully Discrete Galerkin Scheme for the Benjamin-Ono Equation
Sondre Tesdal Galtung
We consider a recently proposed fully discrete Galerkin scheme for the Benjamin-Ono equation which has been found to be locally convergent in finite time for initial data in $L^2(\…