Two new approaches for solving elliptic obstacle problems using discontinuous Galerkin methods

The main aim of this article is to present two new ways solve the elliptic obstacle problem by using discontinuous Galerkin finite element methods. In Gaddam and Gudi (Comput Methods Appl Math 18:223–236, 2018. https://doi.org/10.1515/cmam-2017-0018 ), a bubble enriched conforming quadratic method introduced analyzed for in dimension 3. article, without adding functions, we derive optimal order (with respect regularity) priori error estimates 2 3 localized behavior DG We consider different discrete sets, one with integral constraints motivated from (2018) other nodal at quadrature points. also discuss reliability efficiency proposed posteriori estimator. analysis carried out unified setting which holds several Numerical results are presented illustrate theoretical findings.