Multiblock mortar expanded mixed formulation for second order nonlinear elliptic problems

Abstract

In the present work, we study the numerical approximation of nonlinear elliptic equations using the mortar ex panded mixed method. This framework is based on the mortar finite element method and non-overlapping domain decomposition, allowing independent discretization of each subdomain. An auxiliary interface variable is defined on the internal boundary of subdomains which plays the role of a Dirichlet boundary condition for subdomain problems. This mortar variable also enforces the weak continuity across the interface between subdomains. We combine the multiblock mortar approach with the expanded mixed method to provide accurate approximations for small coefficients. We prove the existence and uniqueness of the discrete problem by employing fixed point argument. Optimal-order convergence estimates are derived for subdomain approximations in the L2 norm. An error bound for the interface approximation is also presented. The computational results matching the theoretical findings are reported.