Abstract. This paper presents an arbitrary order locking-free numerical scheme for linear elasticity on general polygonal/polyhedral partitions by using weak Galerkin (WG) finite element methods. Like other WG methods, the key idea for the linear elasticity is to introduce discrete weak strain and stress tensors which are defined and computed by solving inexpensive local problems on each element. Such local problems are derived from weak formulations of the corresponding differential operators through integration by parts. Locking-free error estimates of optimal order are derived in a discrete H 1 -norm and the usual L 2 -norm for the approximate displacement when the exact solution is smooth. Numerical results are presented to demonstrate the efficiency, accuracy, and the locking-free property of the weak Galerkin finite element method.
Abstract. A weak Galerkin (WG) finite element method for solving the stationary Stokes equations in two-or three-dimensional spaces by using discontinuous piecewise polynomials is developed and analyzed. The variational form we considered is based on two gradient operators which is different from the usual gradient-divergence operators. The WG method is highly flexible by allowing the use of discontinuous functions on arbitrary polygons or polyhedra with certain shape regularity. Optimal-order error estimates are established for the corresponding WG finite element solutions in various norms.Numerical results are presented to illustrate the theoretical analysis of the new WG finite element scheme for Stokes problems.
Flow-induced
translocation of linear and ring polymers is studied
by using a combination of multiparticle collision dynamics and molecular
dynamics. The results show that both end capture and fold capture
are present in the capture process of linear chains in weak flows,
whereas fold capture becomes dominant in strong flows, resulting in
similar behavior for the linear and ring chains in the strong flow
regime. For narrow channels, the critical flux decreases with the
increase of channel size, which is qualitatively consistent with the
prediction by Wu et al.; for large channel sizes (which are still
smaller than the polymer size), the critical flux is independent of
channel size, in agreement with an earlier prediction by de Gennes
et al. The presence of these two scaling regimes indicates that the
confined blob exhibits a crossover from free draining to nondraining
as the channel size increases. Moreover, we found that the conformation
of the polymer exhibits a flow-induced coil–compact–stretch
transition, and the transition does not appear to be first order.
In addition, we observed that the monomers far from the channel and
in the channel exhibit independent dynamics.
This article presents a conforming discontinuous Galerkin (conforming DG) scheme for second order elliptic equations on rectangular partitions. The new method is based on DG finite element space and uses a weak gradient arising from local Raviart Thomas space for gradient approximations. By using the weak gradient and enforcing inter-element continuity strongly, the scheme maintains the simple formulation of conforming finite element method while have the flexibility of using discontinuous approximations. Hence, the programming complexity of this new conforming DG scheme is significantly reduced compared to other existing DG methods. Error estimates of optimal order are established for the corresponding conforming DG approximations in various discrete Sobolev norms. Numerical results are presented to confirm the developed convergence theory.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.