In this work, we introduce a generalization of the enriched Galerkin (EG) method. The key feature our scheme is an adaptive two-mesh approach that, in addition to standard enrichment conforming finite element discretization via discontinuous degrees freedom, allows subdivide selected (e.g. troubled) mesh cells non-conforming fashion and use further on finer submesh. We prove stability sharp pri...

Abstract The explosive welding process is an extreme-deformation problem that involves shock waves, large plastic deformation, and fragmentation around the collision point, which are extremely challenging features to model for traditional mesh-based methods. In this work, a particle-based Godunov algorithm under semi-Lagrangian reproducing kernel particle method (SL-RKPM) introduced into volume...

For the efficient numerical solution of indefinite linear systems arising from curl conforming edge element approximations of the time-harmonic Maxwell equation, we consider local multigrid methods (LMM) on adaptively refined meshes. The edge element discretization is done by the lowest order edge elements of Nédélec's first family. The LMM features local hybrid Hiptmair smoothers of Jacobi and...

We consider the conforming of finite element approximations of reactiondiffusion problems. We propose new a posteriori error estimators based on H(div)conforming finite elements and equilibrated fluxes. It is shown that these estimators give rise to an upper bound where the constant is one in front of the indicator, up to higher order terms. Lower bounds can also be established with constants d...

In this paper, conforming finite elements on polygon meshes are developed. Polygonal finite elements provide greater flexibility in mesh generation and are better-suited for applications in solid mechanics which involve a significant change in the topology of the material domain. In this study, recent advances in meshfree approximations, computational geometry, and computer graphics are used to...

“Discrete Duality Finite Volume” schemes (DDFV for short) on general 2D meshes, in particular non conforming ones, are studied for the Stokes problem with Dirichlet boundary conditions. The DDFV method belongs to the class of staggered schemes since the components of the velocity and the pressure are approximated on different meshes. In this paper, we investigate from a numerical and theoretica...

In this paper, the quadtree data structure and conforming polygonal interpolants are used to develop an h-adaptive finite element method. Quadtree is a hierarchical data structure that is computationally attractive for adaptive numerical simulations. Mesh generation and adaptive refinement of quadtree meshes is straight-forward. However, finite elements are non-conforming on quadtree meshes due...

We describe a high-order accurate space-time discontinuous Galerkin (DG) method for solving compressible flow problems on two-dimensional moving domains with large deformations. The DG discretization and space-time numerical fluxes are formulated on a three-dimensional space-time domain. The scheme is implicit, and we solve the resulting non-linear systems using a parallel Newton-Krylov solver....