dc.contributor.advisor Holden, Helge dc.contributor.author Galtung, Sondre Tesdal dc.date.accessioned 2016-06-30T14:00:32Z dc.date.available 2016-06-30T14:00:32Z dc.date.created 2016-06-10 dc.date.issued 2016 dc.identifier ntnudaim:15775 dc.identifier.uri http://hdl.handle.net/11250/2395092 dc.description.abstract In this thesis 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 based on a recent result for a similar numerical method for the Korteweg--de Vries equation, and utilises a commutator estimate related to a local smoothing effect to bound the $H^{\frac{1}{2}}$-norm of the approximations locally. This enables us to show that the scheme converges strongly in $L^{2}(0,T;L^{2}_{\text{loc}}(\mathbb{R}))$ to a weak solution of the equation for initial data in $L^{2}$ and some $T > 0$. Finally we illustrate the convergence with some numerical examples. dc.language eng dc.publisher NTNU dc.subject Fysikk og matematikk, Industriell matematikk dc.title A Convergent Crank-Nicolson Galerkin Scheme for the Benjamin-Ono Equation dc.type Master thesis dc.source.pagenumber 73
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