Convergence analysis of a modified weak Galerkin finite element method for Signorini and obstacle problems

Abstract

In this article, we apply a modified weak Galerkin method to solve variational inequality of the first kind which includes Signorini and obstacle problems. Optimal order a priori error estimates in the energy norm are derived. We also provide some numerical experiments to validate the theoretical results.© 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1459–1474, 2017

A modified weak Galerkin method for $\boldsymbol{H}(\mathrm{curl})$-elliptic problem

“…Comparing with WG method, MWG method contains less unknowns, while the accuracy stays the same. Then, MWG method has also found its way to other problems, such as the parabolic problems [3], Sobolev equation [4], Signorini and obstacle problems [27], Stokes problem [18,16] and poroelasticity problem [25]. However, to our best knowledge, there are not any published literatures for the MWG discretization of H(curl) elliptic problem.…”

The augmented Lagrangian method as a framework for stabilised methods in computational mechanics

“…For stabilised finite element methods in the context of variational inequalities see [5,71,75,66,59,60,62]. More recently discontinuous Galerkin methods and other non-conforming methods allowing for polygonal elements have been developed for different types of contact problems [100,99,28,106,107,53,101,39]. Another recent development is the application of isogeometric analysis to contact problems [98,41,77,2].…”

Convergence of an adaptive modified WG method for second-order elliptic problem

“…Comparing with WG methods, MWG methods contain less unknowns, while the accuracy stays the same. Then, MWG method has also found its way to other problems, such as the parabolic problems [11], Sobolev equation [12], Signorini and obstacle problems [37], Stokes problem [27]. The solution of (3) may contain singularity.…”