Abstract
In this article, a priori and a posteriori estimates of conforming and expanded mixed finite element methods for a Kirchhoff equation
of elliptic type are derived. For the expanded mixed finite element method, a variant of Brouwer’s fixed point argument combined with a monotonicity argument yields the well-posedness of the discrete nonlinear system. Further, a use of both Helmholtz decomposition of
Funding statement: The first author acknowledges the financial support of the Council of Scientific and Industrial Research (CSIR), Government of India (CSIR Sr.No. 09/087(0599)/2010-EMR-I). The second author gratefully acknowledges the research support of the Department of Science and Technology, Government of India, through the National Programme on Differential Equations: Theory, Computation and Applications, DST project no. SERB/F/1279/2011-2012.
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