Η ασυνεχή μέθοδο Galerkin για την μη γραμμική εξίσωση του schrodinger στην κρίσιμη διάσταση
Adaptive discontinuous Galerkin finite elements method for the non linear Schrodinger equation
Γουρζουλίδης, Δημήτριος
Πλεξουσάκης, Μιχαήλ
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.
(EN)
