Because of the best approximation property, traditional Bubnov–Galerkin numerical
methods have proven immensely successful in modeling self-adjoint problems, such as heat …

由于无网格法中大多数近似函数均为有理式, 不具有Kronecker delta 性质, 因此难以精确地施加
本质边界条件. 边界误差较大容易导致整个求解域求解结果精度低, 甚至引起数值不稳定现象 …

The material point method (MPM) suffers from poor accuracy and suboptimal convergence
rates compared to other numerical methods due to the under-integration of the weak form; …

A generalized variational principle with five independent variables is proposed for strain
gradient elasticity, including displacement, strain, strain gradient, stress, and double stress …

An efficient and inherently consistent integration method, named projection integration (PI),
is proposed for Galerkin meshfree methods with arbitrary order. In contrast to traditional …

Abstract Moving Least Squares (MLS), as a series representation type of approximation, is
broadly used in a wide array of meshfree methods. However, using the existing standard …

An improved naturally stabilized nodal integration (NSNI) is presented for resolving
displacement locking concerned with highly orthotropic and nearly incompressible materials …

Physics informed neural network (PINN) frameworks have been developed as a powerful
technique for solving partial differential equations (PDEs) with potential data integration …

Since most of the approximation functions in the meshfree method are rational and do not
have the Kronecker delta property, it is difficult to accurately impose the essential boundary …

This paper presents a new two level local projection meshfree stabilization (LPMS) method
under the classical stabilized conforming nodal integration (SCNI) framework to solve …