Browsing Mathematics, Statistics, and Physics by Subject "Adaptivity"

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

Huang, Juntao; Liu, Yuan; Guo, Wei; Tao, Zhanjing; Cheng, Yingda (Springer, 2020-10-04)

In this paper, we propose a class of adaptive multiresolution (also called adaptive sparse grid) discontinuous Galerkin (DG) methods for simulating scalar wave equations in second order form in space. The two key ingredients ...
An adaptive multiresolution ultra-weak discontinuous Galerkin method for nonlinear Schrödinger equations

Tao, Zhanjing; Huang, Juntao; Liu, Yuan; Guo, Wei; Cheng, Yingda (Springer, 2021-01-25)

This paper develops a high-order adaptive scheme for solving nonlinear Schrödinger equations. The solutions to such equations often exhibit solitary wave and local structures, which make adaptivity essential in improving ...