A Convergent Crank-Nicolson Galerkin Scheme for the Benjamin-Ono Equation
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 |