Abstract
We introduce a domain decomposition structure-preserving method based on a hybrid mimetic spectral element method for three-dimensional linear elasticity problems in curvilinear conforming structured meshes. The method is an equilibrium method which satisfies pointwise equilibrium of forces. The domain decomposition is established through hybridization which first allows for an inter-element normal stress discontinuity and then enforces the normal stress continuity using a Lagrange multiplier which turns out to be the displacement in the trace space. Dual basis functions are employed to simplify the discretization and to obtain a higher sparsity. Numerical tests supporting the method are presented.
Highlights
Structure-preserving or mimetic methods are numerical methods that aim to preserve fundamental properties of the continuous problems, like conservation laws, at the discrete level
We introduce a hybrid mimetic spectral element method based on a new hybrid variational principle for three-dimensional linear elasticity problems
It can be seen that the hybrid mimetic spectral element method (hMSEM) and the mimetic spectral element method (MSEM) have the same accuracy with respect to the L2-error of the solutions uh, ωh, and σ h for different basis function degrees (N = 1, 3) and element densities (K = 2, 4, 6) regardless of whether we are considering orthogonal meshes (c = 0) or heavily distorted meshes (c = 0.25)
Summary
Structure-preserving or mimetic methods are numerical methods that aim to preserve fundamental properties of the continuous problems, like conservation laws (for example equilibrium of forces in elasticity), at the discrete level. One of the main problems in hybrid finite element methods is the appearance of so-called spurious kinematic modes or zero energy modes, see, for instance, [27,28,29]. These spurious modes consist of non-solid body deformations which do not affect the stress field indicating that such hybrid formulations are non-wellposed. We introduce a hybrid mimetic spectral element method (hMSEM) based on a new hybrid variational principle for three-dimensional linear elasticity problems.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
