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We consider a nonlinear parabolic PDE that describes the evolution of the surface morphology in the deposition of thin glassy films by molecular beam epitaxy. Due to the dynamics of the growth process which exhibits some unexpected initial linear behavior, for the numerical solution we suggest a combined spectral element/finite element approach. The results of numerical simulations are in good agreement with experimental measurements and show a superior performance of the chosen method compared to more traditional techniques.

journal of numerical mathematics

A combined spectral element/finite element approach to the numerical solution of a nonlinear evolution equation describing amorphous surface growth of thin films