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This paper presents and studies an approach for constructing auxiliary spacepreconditioners for finite element problems using a constrained nonconformingreformulation, that is based on a proposed modified version of the mortarmethod. The well-known mortar finite element discretization method is modifiedto admit a local structure, providing an element-by-element orsubdomain-by-subdomain assembly property. This is achieved via the introductionof additional trace finite element spaces and degrees of freedom (unknowns)associated with the interfaces between adjacent elements or subdomains. Theresulting nonconforming formulation and a reduced via static condensation Schurcomplement form on the interfaces are used in the construction of auxiliaryspace preconditioners for a given conforming finite element discretizationproblem. The properties of these preconditioners are studied and theirperformance is illustrated on model second order scalar elliptic problemsutilizing high order elements.

A Condensed Constrained Nonconforming Mortar-based Approach for Preconditioning Finite Element Discretization Problems