A meshless Galerkin method for non-local diffusion using localized kernel bases Academic Article uri icon

abstract

  • © 2018 American Mathematical Society. We introduce a meshless method for solving both continuous and discrete variational formulations of a volume constrained, non-local diffusion problem. We use the discrete solution to approximate the continuous solution. Our method is non-conforming and uses a localized Lagrange basis that is constructed out of radial basis functions. By verifying that certain inf-sup conditions hold, we demonstrate that both the continuous and discrete problems are well-posed, and also present numerical and theoretical results for the convergence behavior of the method. The stiffness matrix is assembled by a special quadrature routine unique to the localized basis. Combining the quadrature method with the localized basis produces a well-conditioned, symmetric matrix. This then is used to find the discretized solution.

author list (cited authors)

  • Lehoucq, R. B., Narcowich, F. J., Rowe, S. T., & Ward, J. D.

citation count

  • 2

publication date

  • February 2018