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Identifier

000398263

Title

Adaptive discontinuous Galerkin finite elements method for the non linear Schrodinger equation

Alternative Title

Η ασυνεχή μέθοδο Galerkin για την μη γραμμική εξίσωση του schrodinger στην κρίσιμη διάσταση

Author

Γουρζουλίδης, Δημήτριος

Thesis advisor

Πλεξουσάκης, Μιχαήλ

Abstract

We consider an initial-value problem for the nonlinear Schrodinger with cubic nonlinear-ity in the critical dimension (d = 2). To approximate smooth solutions of this problem we construct and analyse a numerical method where the spatial discretization is based on discontinuous Galerkin finite elements and the temporal discretization is achieved by the implicit Crack-Nickolson scheme. We then equip this scheme with an adaptive spatial and temporal mesh refinement mechanism that enables the numerical technique to ap¬proximate well singular solutions of the NLS equation up to times close to blow-up. The numerical method presented here aims to approximate both radially and non-radially solutions of the NLS.

Language

English

Subject

Πεπερασμένα στοιχεία

Issue date

2015-11-20

Collection

School/Department--School of Sciences and Engineering--Department of Mathematics and Applied Mathematics--Post-graduate theses

Type of Work--Post-graduate theses

Views

407

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