Lehoucq, The exit-time problem for a Markov jump process, The European Physical Journal Special Topics 223 (2014), no. Ridgway Scott, The mathematical theory of finite element methods, 3rd ed., Texts in Applied Mathematics, vol. 15, Springer, New York, 2008. Rowe, A Galerkin radial basis function method for nonlocal diffusion, Meshfree methods for partial differential equations VII, Lect. Osborn, Survey of meshless and generalized finite element methods: a unified approach, Acta Numer.
Burak Aksoylu and Tadele Mengesha, Results on nonlocal boundary value problems, Numer.65, Academic Press, New York-London, 1975. Adams, Sobolev spaces, Pure and Applied Mathematics, Vol. Gabriel Acosta and Juan Pablo Borthagaray, A fractional Laplace equation: regularity of solutions and finite element approximations, SIAM J.Academy for Advanced Telecommunications and Learning Technologies, Texas A&M University Brazos HPC,, 2015.This then is used to find the discretized solution. Combining the quadrature method with the localized basis produces a well-conditioned, symmetric matrix. The stiffness matrix is assembled by a special quadrature routine unique to the localized basis. 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. Our method is non-conforming and uses a localized Lagrange basis that is constructed out of radial basis functions. We use the discrete solution to approximate the continuous solution. We introduce a meshless method for solving both continuous and discrete variational formulations of a volume constrained, non-local diffusion problem. HTML articles powered by AMS MathViewer by A meshless Galerkin method for non-local diffusion using localized kernel bases
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