6 papers
Finite element exponential integration for rough solutions of nonlinear wave equations. Part II: Dynamic boundary conditions on curved domains
Jiachuan Cao, Benjamin Dörich, Buyang Li
We study nonlinear wave equations with dynamic boundary conditions on smooth bounded domains and analyze a fully discrete approximation in the low-regularity regime. The method com…
Finite element exponential integration for rough solutions of nonlinear wave equations. Part I: Dirichlet boundary conditions on polygonal and polyhedral domains
Jiachuan Cao, Benjamin Dörich, Marlis Hochbruck +1
We study a fully discrete scheme for nonlinear wave equations on general bounded polygonal/polyhedral domains with initial data , $0<γ\le…
A neural network method for scalar conservation laws with convergence rates for shock-wave solutions
Jiachuan Cao, Buyang Li, Hao Li
We propose a new entropy-compatible neural network method for scalar hyperbolic conservation laws and establish, to our knowledge, the first explicit \(L^1\) convergence rates in t…
Computing rough solutions of the KdV equation below
Jiachuan Cao, Buyang Li, Yifei Wu +1
We establish a novel numerical and analytical framework for solving the Korteweg--de Vries (KdV) equation in the negative Sobolev spaces, where classical numerical methods fail due…
Computing rough solutions of the stochastic nonlinear wave equation
Jiachuan Cao, Buyang Li, Katharina Schratz
The regularity of solutions to the stochastic nonlinear wave equation plays a critical role in the accuracy and efficiency of numerical algorithms. Rough or discontinuous initial c…
Numerical approximation of discontinuous solutions of the semilinear wave equation
Jiachuan Cao, Buyang Li, Yanping Lin +1
A high-frequency recovered fully discrete low-regularity integrator is constructed to approximate rough and possibly discontinuous solutions of the semilinear wave equation. The pr…