Recovered finite element methods on polygonal and polyhedral meshes
Provides a new conforming discretization framework for general polygonal/polyhedral meshes, benefiting computational mechanics and PDE solvers.
This work extends recovered finite element methods (R-FEM) to polygonal and polyhedral meshes, achieving conforming discretizations with degrees of freedom comparable to discontinuous Galerkin methods. A priori error bounds are proven for linear advection-diffusion-reaction problems, and numerical experiments demonstrate good performance.
Recovered finite element methods (R-FEM) have been recently introduced for meshes consisting of simplicial and/or box-type meshes. Here, utilising the flexibility of R-FEM framework, we extend their definition on polygonal and polyhedral meshes in two and three spatial dimensions, respectively. A key attractive feature of this framework is its ability to produce conforming discretizations, yet involving only as many degrees of freedom as discontinuous Galerkin methods over general polygonal/polyhedral meshes with potentially many faces per element. A priori error bounds are shown for general linear, possibly degenerate, second order advection-diffusion-reaction boundary value problems. A series of numerical experiments highlights the good practical performance of the proposed numerical framework.