In this work finite superelements method (FSEM) for solution of biharmonic equation in bounded domains is proposed and developed. The method is based on decomposition of domain into subdomains with the solution of a number of intermediary problems, every of which is a boundary value problem for biharmonic equation with boundary condition being basis for interpolation of solution at superelements boundaries. The initial problem solution is found as an expansion on the constructed function system. It is shown that the solution of general problem can be recovered using functions and traces found above. Error estimates for one case of FSEM are obtained.
Galanin, M., Milyutin, D., & Savenkov, E. (2007). Finite superelements method for biharmonic equation. Mathematical Modelling and Analysis, 12(3), 309-324. https://doi.org/10.3846/1392-6292.2007.12.309-324
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