2020/11/10 by Lina Zhao, Eric Chung, Zhao, Lina +5 · 3 citations
Computer Science · Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Applied mathematics #Biot number #Computational Fluid Dynamics and Aerodynamics #Computer science #Convergence (economics) #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Geometry #Mathematical analysis #Mathematical optimization #Mathematics #Mechanics #Numerical Analysis (math.NA) #Physics #Piecewise #Polygon mesh #Poromechanics #Porous medium #Rate of convergence #cs.NA #math.NA
paper · pdf · doi:10.48550/arxiv.2011.04924
published in arXiv (Cornell University) (Cornell University) · 29 pages
arxiv created 2020/11/10 · openalex publication_date 2020/11/10 · arxiv updated 2020/11/11 · openalex created_date 2020/11/23 · openalex updated_date 2026/08/01
In this paper we propose and analyze a staggered discontinuous Galerkin method for a five-field formulation of the Biot system of poroelasticity on general polygonal meshes. Elasticity is equipped with stress-displacement-rotation formulation with weak stress symmetry for arbitrary polynomial orders, which extends the piecewise constant approximation developed in (L. Zhao and E.-J. Park, SIAM J. Sci. Comput. 42 (2020), A2158-A2181). The proposed method is locking free and can handle highly distorted grids possibly including hanging nodes, which is desirable for practical applications. We prove the convergence estimates for the semi-discrete scheme and fully discrete scheme for all the variables in their natural norms. In particular, the stability and convergence analysis do not need a uniformly positive storativity coefficient. Moreover, to reduce the size of the global system, we propose a five-field formulation based fixed stress splitting scheme, where the linear convergence of the scheme is proved. Several numerical experiments are carried out to confirm the optimal convergence rates and the locking-free property of the proposed method.