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We present a class of nonconforming virtual element methods for generalfourth order partial differential equations in two dimensions. We develop ageneric approach for constructing the necessary projection operators andvirtual element spaces. Optimal error estimates in the energy norm are providedfor general linear fourth order problems with varying coefficients. We alsodiscuss fourth order perturbation problems and present a novel nonconformingscheme which is uniformly convergent with respect to the perturbation parameterwithout requiring an enlargement of the space. Numerical tests are carried outto verify the theoretical results. We conclude with a brief discussion on howour approach can easily be applied to nonlinear fourth order problems.

Robust nonconforming virtual element methods for general fourth order problems with varying coefficients