Log In Sign Up

An adaptive multiresolution ultra-weak discontinuous Galerkin method for nonlinear Schrodinger equations

by   Zhanjing Tao, et al.

This paper develops a high order adaptive scheme for solving nonlinear Schrodinger equations. The solutions to such equations often exhibit solitary wave and local structures, which makes adaptivity essential in improving the simulation efficiency. Our scheme uses the ultra-weak discontinuous Galerkin (DG) formulation and belongs to the framework of adaptive multiresolution schemes. Various numerical experiments are presented to demonstrate the excellent capability of capturing the soliton waves and the blow-up phenomenon.


page 15

page 16

page 17

page 18

page 21

page 22

page 23


p-adaptive algorithms in Discontinuous Galerkin solutions to the time-domain Maxwell's equations

The Discontinuous Galerkin time-domain method is well suited for adaptiv...

A discontinuous Galerkin method for nonlinear biharmonic Schrödinger equations

This paper proposes and analyzes an ultra-weak local discontinuous Galer...

An adaptive multiresolution interior penalty discontinuous Galerkin method for wave equations in second order form

In this paper, we propose a class of adaptive multiresolution (also call...

Stabilizing discontinuous Galerkin methods using Dafermos' entropy rate criterion

A novel approach for the stabilization of the discontinuous Galerkin met...

Adaptive Third Order Adams-Bashforth Time Stepping Scheme for 2D Extended Boussinesq Equations

We develop the third-order adaptive Adams-Bashforth time stepping scheme...