Hybrid coupling of CG and HDG discretizations based on Nitsche's method
arXiv:1906.10711 · doi:10.1007/s00466-019-01770-8
Abstract
A strategy to couple continuous Galerkin (CG) and hybridizable discontinuous Galerkin (HDG) discretizations based only on the HDG hybrid variable is presented for linear thermal and elastic problems. The hybrid CG-HDG coupling exploits the definition of the numerical flux and the trace of the solution on the mesh faces to impose the transmission conditions between the CG and HDG subdomains. The continuity of the solution is imposed in the CG problem via Nitsche's method, whereas the equilibrium of the flux at the interface is naturally enforced as a Neumann condition in the HDG global problem. The proposed strategy does not affect the core structure of CG and HDG discretizations. In fact, the resulting formulation leads to a minimally-intrusive coupling, suitable to be integrated in existing CG and HDG libraries. Numerical experiments in two and three dimensions show optimal global convergence of the stress and superconvergence of the displacement field, locking-free approximation, as well as the potential to treat structural problems of engineering interest featuring multiple materials with compressible and nearly incompressible behaviors.
arXiv comment28 pages, 14 figures
References in corpus (10)
- A Hybrid High-Order method for the incompressible Navier--Stokes equations based on Temam's device
- Hybrid High-Order methods for finite deformations of hyperelastic materials
- Mixed-Hybrid and Vertex-Discontinuous-Galerkin Finite Element Modeling of Multiphase Compositional Flow on 3D Unstructured Grids
- A super--convergent hybridisable discontinuous Galerkin method for linear elasticity
- A superconvergent HDG method for Stokes flow with strongly enforced symmetry of the stress tensor
- A locking-free face-centred finite volume (FCFV) method for linear elasticity
- A Hybrid High-Order method for incremental associative plasticity with small deformations
- A hybrid finite volume -- finite element method for bulk--surface coupled problems
- Discontinuous Galerkin approximations in computational mechanics: hybridization, exact geometry and degree adaptivity
- An equilibrated fluxes approach to the certified descent algorithm for shape optimization using conforming finite element and discontinuous Galerkin discretizations
Cited by in corpus (6)
- A weakly compressible hybridizable discontinuous Galerkin formulation for fluid-structure interaction problems
- HDGlab: An open-source implementation of the hybridisable discontinuous Galerkin method in MATLAB
- Discontinuous Galerkin approximations in computational mechanics: hybridization, exact geometry and degree adaptivity
- A non-oscillatory face-centred finite volume method for compressible flows
- Benchmarking the face-centred finite volume method for compressible laminar flows
- A hybridizable discontinuous Galerkin method for electromagnetics with a view on subsurface applications