10 papers · 1 filter
Finite element methods for isometric embedding of Riemannian manifolds
Guangwei Gao, Kaibo Hu, Buyang Li +1
The isometric embedding problem for Riemannian manifolds, which connects intrinsic and extrinsic geometry, is a central question in differential geometry with deep theoretical sign…
Convergence and Stability of Discrete Exterior Calculus for the Hodge Laplace Problem in Two Dimensions
Chengbin Zhu, Snorre H. Christiansen, Kaibo Hu +1
We prove convergence and stability of the discrete exterior calculus (DEC) solutions for the Hodge-Laplace problems in two dimensions for families of meshes that are non-degenerate…
Many facets of cohomology: Differential complexes and structure-aware formulations
Kaibo Hu
Complexes and cohomology, traditionally central to topology, have emerged as fundamental tools across applied mathematics and the sciences. This survey explores their roles in dive…
Finite element form-valued forms: Construction
Kaibo Hu, Ting Lin
We provide a finite element discretization of -form-valued -forms on triangulation in for general , and and any polynomial degree. The const…
Helicity-preserving finite element discretization for magnetic relaxation
Mingdong He, Patrick E. Farrell, Kaibo Hu +1
The Parker conjecture, which explores whether magnetic fields in perfectly conducting plasmas can develop tangential discontinuities during magnetic relaxation, remains an open que…
Error estimates for a helicity-preserving finite element discretisation of an incompressible magnetohydrodynamics system
L. Beirao da Veiga, K. Hu, L. Mascotto
We derive error estimates of a finite element method for the approximation of solutions to a seven-fields formulation of a magnetohydrodynamics model, which preserves the energy of…