Search Results

• On Residual Minimization for PDEs: Failure of PINN, Modified Equation, and Implicit Bias

  Tao Luo, Qixuan Zhou

  2026-01-21

  440 138 Pages:313-376

• Estimates for Green's Functions of Elliptic Equations in Non-Divergence Form with Continuous Coefficients

  Seick Kim, Sungjin Lee

  2021-07-30

  36765 3515 Pages:111-130

• Application of the Alternating Direction Method of Multipliers to Control Constrained Parabolic Optimal Control Problems and Beyond

  Roland Glowinski, Yongcun Song, Xiaoming Yuan, Hangrui Yue

  2022-04-15

  43677 3159 Pages:115-158

• Improved Analysis of PINNs: Alleviate the CoD for Compositional Solutions

  Yuling Jiao, Xiliang Lu, Jerry Zhijian Yang, Cheng Yuan, Pingwen Zhang

  2023-09-15

  30387 2856 Pages:239-263

• A Survey on the Performance of Krylov Subspace Methods in High Order Compact Schemes for Solving Poisson’s Equation for Application in Incompressible Fluid Flow Solvers

  Iman Farahbakhsh, Benyamin Barani Nia, Mehdi Dehghan

  2025-06-04

  9913 618 Pages:239-266

• The Method of Fundamental Solutions for Optical Fluorescence

  Andreas Karageorghis, Daniel Lesnic

  2025-06-04

  9998 599 Pages:219-238

• A Canonical Construction of $H^m$-Nonconforming Triangular Finite Elements

  Jun Hu, Shangyou Zhang

  2022-06-21

  24522 2882 Pages:266-288

• Boundary Homogenization of a Class of Obstacle Problems

  Jingzhi Li, Hongyu Liu, Lan Tang, Jiangwen Wang

  2022-04-15

  41152 3289 Pages:240-260 Open-access

• Multiple Vortices for the Shallow Water Equation in Two Dimensions

  Daomin Cao, Zhongyuan Liu

  2020-08-24

  39739 3193 Pages:221-249