• Corpus ID: 220962227

A general approach for constructing robust virtual element methods for fourth order problems

@article{Dedner2020AGA,
  title={A general approach for constructing robust virtual element methods for fourth order problems},
  author={Andreas Dedner and Alice Hodson},
  journal={ArXiv},
  year={2020},
  volume={abs/2008.01617}
}

• A. Dedner, Alice Hodson
• Published 4 August 2020
• Mathematics
• ArXiv

We present a class of nonconforming virtual element methods for general fourth order partial differential equations in two dimensions. We develop a generic approach for constructing the necessary projection operators and virtual element spaces. Optimal error estimates in the energy norm are provided for general linear fourth order problems with varying coefficients. We also discuss fourth order perturbation problems and present a novel nonconforming scheme which is uniformly convergent with respect to the perturbation parameter without requiring an enlargement of the space. Numerical tests are carried out to verify the theoretical results. We conclude with a brief discussion on how our approach can easily be applied to nonlinear fourth order problems.