A talk given by A. Ortiz-Bernardin at POEMS 2017: Workshop on Polytopal Element Methods in Mathematics and Engineering, July 6, 2017, Milan, Italy.
Consistent and Stable Meshfree Galerkin Methods Using The Virtual Element Decomposition
Alejandro Ortiz-Bernardin
Department of Mechanical Engineering, University of Chile
Av. Beauchef 851, Santiago, 8370456, Chile
aortizb@ing.uchile.cl
ABSTRACT
In the numerical solution of partial differential equations, meshfree Galerkin methods are numerical methods that use a cloud of nodes for domain discretization. Smooth nonpolynomial basis functions are constructed using this nodal discretization. Even though these methods do not need an underlying mesh structure for construction of the nodal basis functions, they require a background mesh to perform the numerical integration of the Galerkin weak form integrals. Due to the nonpolynomial character of the meshfree nodal basis functions, there exist inaccuracies in the numerical integration, which affects the consistency and stability of the method. This talk summarizes current developments in meshfree Galerkin methods that use the mathematical framework of the virtual element method to tackle the numerical integration issue.