Title: A priori error estimates of multiblock mortar expanded mixed method for elliptic problems
Abstract: The multiblock mortar expanded mixed method is explored to solve the second order linear elliptic problem. In this method, the domain is expressed as a union of smaller blocks (subdomains) separated by interface. The original problem is posed on each block and discretized locally. A scalar unknown is introduced on the shared boundaries between the blocks which is treated as Dirichlet boundary condition for the local problem. A special finite element space is constructed on the interface which serve as Lagrange multiplier to impose flux continuity across the inter-block boundaries. The mortar space is also used to approximate the scalar variable introduced on interface. We applied expanded mixed method to solve the local problem on each block and derived the error estimates for scalar, its gradient and its flux. We established the optimal order convergence rates for subdomain approximations. An error bound for mortar pressure is also presented. The computation is performed by transforming the algebraic system encounter by formulation into the positive definite problem in mortar space. An algorithm illustrating the implementation of method is also provided. The numerical experiments confirming theoretical results are also provided.
Publication Year: 2020
Publication Date: 2020-11-01
Language: en
Type: article
Indexed In: ['crossref']
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Cited By Count: 2
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