SIAM Journal on Numerical Analysis · 2022 · 17 citations · 14 references
EngineeringMathematicsComplex SystemsFinite Element AnalysisFinite Element MethodsFinite Element DiscretizationFinite Element FormulationComplex Differential GeometryConforming Finite ElementsDual Variational FormulationFinite Element SpacesFinite Element Weak FormGridsLinearized Einstein EquationsTetrahedral Complexes
This paper presents the first family of conforming finite element $\ddiv\ddiv$ complexes on tetrahedral grids in three dimensions. In these complexes, finite element spaces of $H(\ddiv\ddiv,\Omega;\Sbb)$ are from a recent article [L. Chen and X. Huang, Math. Comp., 91 (2022), pp. 1107--1142] while finite element spaces of both $H(\sym\ccurl,\Omega;\Tbb)$ and $H^1(\Omega;\R^3)$ are newly constructed here. It is proved that these finite element complexes are exact. As a result, they can be used to discretize the linearized Einstein--Bianchi system within the dual formulation.
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