hp-adaptive celatus enriched discontinuous Galerkin method for second-order elliptic source problems.

Abstract

This paper presents a new way to enrich finite element methods with nonpolynomial functions without adding any function to the finite element space. For this reason, the method is called celatus, which is a Latin word meaning ``hidden from view."" Since no nonpolynomial function is added to the finite element space, many issues with standard enriched methods are avoided, among which there is the worsening of the condition of the linear system. In the present work, we focus on second-order elliptic source problems with reentering corners and show that the new method is more computationally efficient than standard finite element methods when used with hp-adaptivity.