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Numerical analysis of the meshless element-free Galerkin method for hyperbolic initial-boundary value problems

Yaozong Tang;  Xiaolin Li — 2017

Applications of Mathematics

The meshless element-free Galerkin method is developed for numerical analysis of hyperbolic initial-boundary value problems. In this method, only scattered nodes are required in the domain. Computational formulae of the method are analyzed in detail. Error estimates and convergence are also derived theoretically and verified numerically. Numerical examples validate the performance and efficiency of the method.

Boundary augmented Lagrangian method for the Signorini problem

Shougui Zhang;  Xiaolin Li — 2016

Applications of Mathematics

An augmented Lagrangian method, based on boundary variational formulations and fixed point method, is designed and analyzed for the Signorini problem of the Laplacian. Using the equivalence between Signorini boundary conditions and a fixed-point problem, we develop a new iterative algorithm that formulates the Signorini problem as a sequence of corresponding variational equations with the Steklov-Poincaré operator. Both theoretical results and numerical experiments show that the method presented...

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