12 papers
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…
Hodge-Dirac wave systems and structure-preserving discretizations of the linearized Einstein equations
Marien-Lorenzo Hanot, Kaibo Hu
We derive a reformulation of the linearized Arnowitt-Deser-Misner (ADM) equations as a Hodge-Dirac wave system with the divdiv complex, addressing challenges in numerical relativit…
A 2-complex containing Sobolev spaces of matrix fields
Jay Gopalakrishnan, Kaibo Hu, Joachim Schöberl
Using a generalization of complexes, called 2-complexes, this paper defines and analyzes new Sobolev spaces of matrix fields and their interrelationships within a commuting diagram…
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…
Quadratic and cubic Lagrange finite elements for mixed Laplace eigenvalue problems on criss-cross meshes
Kaibo Hu, Jiguang Sun, Qian Zhang
In [6], it was shown that the linear Lagrange element space on criss-cross meshes and its divergence exhibit spurious eigenvalues when applied in the mixed formulation of the Lapla…
Extended Regge complex for linearized Riemann-Cartan geometry and cohomology
Snorre H. Christiansen, Kaibo Hu, Ting Lin
We show that the cohomology of the Regge complex in three dimensions is isomorphic to , the infinitesimal-rigid…
Distributional Hessian and divdiv complexes on triangulation and cohomology
Kaibo Hu, Ting Lin, Qian Zhang
In this paper, we construct discrete versions of some Bernstein-Gelfand-Gelfand (BGG) complexes, i.e., the Hessian and the divdiv complexes, on triangulations in 2D and 3D. The seq…
Finite elements for symmetric and traceless tensors in three dimensions
Kaibo Hu, Ting Lin, Bowen Shi
We construct a family of finite element sub-complexes of the conformal complex on tetrahedral meshes and show their exactness on contractible domains. This complex includes vector…