Interest in meshfree methods in solving boundary-value problems has grown rapidly in recent years. A meshless method that has attracted considerable interest in the community of computational mechanics is built around the idea of modified local Shepard’s partition of unity. For these kinds of applications it is fundamental to analyze the order of the approximation in the context of Sobolev spaces. In this paper, we study two different techniques for building modified local Shepard’s formulas, and...

In this paper, the Babuška’s theory of Lagrange multipliers is extended to higher order elliptic Dirichlet problems. The resulting variational formulation provides an efficient numerical squeme in meshless methods for the approximation of elliptic problems with essential boundary conditions.

In this paper, the Babuška's theory of Lagrange multipliers is extended
to higher order elliptic Dirichlet problems. The resulting variational
formulation provides an efficient numerical squeme in meshless methods for
the approximation of elliptic problems with essential boundary conditions.

Interest in meshfree methods in solving boundary-value problems has grown
rapidly in recent years. A meshless method that has attracted considerable
interest in the community of computational mechanics is built around the
idea of modified local Shepard's partition of unity. For these kinds of
applications it is fundamental to analyze the order of the approximation in
the context of Sobolev spaces. In this paper, we study two different
techniques for building modified local Shepard's formulas, and...

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