5 papers
Error estimates for vector field interpolation based on generalized matrix-valued kernels
Zhengjie Sun, Lishuo Dong, Leevan Ling
Matrix-valued kernels provide a flexible framework for approximating vector fields from scattered data, especially when structural constraints such as divergence-free or curl-free…
Energy-conserving Kansa methods for Hamiltonian wave equations
Xiaobin Li, Meng Chen, Zhengjie Sun +2
We introduce a fast, constrained meshfree solver designed specifically to inherit energy conservation (EC) in second-order time-dependent Hamiltonian wave equations. For discretiza…
Inverse inequalities for kernel-based approximation on bounded domains and Riemannian manifolds
Zhengjie Sun, Leevan Ling
This paper establishes inverse inequalities for kernel-based approximation spaces defined on bounded Lipschitz domains in and compact Riemannian manifolds. While inv…
Structure-preserving Kernel-based methods for solving dissipative PDEs on surfaces
Zhengjie Sun, Leevan Ling, Meng Chen
In this paper, we propose a general meshless structure-preserving Galerkin method for solving dissipative PDEs on surfaces. By posing the PDE in the variational formulation and sim…
Proving the stability estimates of variational least-squares Kernel-Based methods
Meng Chen, Leevan Ling, Dongfang Yun
Motivated by the need for the rigorous analysis of the numerical stability of variational least-squares kernel-based methods for solving second-order elliptic partial differential…