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An adaptive multiresolution ultra-weak discontinuous Galerkin method for nonlinear Schrodinger equations
Zhanjing Tao, Juntao Huang, Yuan Liu, Wei Guo, Yingda Cheng
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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.
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