Abstract
The Localized Adjoint Method (LAM) is a new and promising methodology for discretizing partial differential equations, which is based on Herrera’s Algebraic Theory of Boundary Value Problems. A large number of numerical applications have already been made. Herera’s Algebraic Theory implies a kind of operator extensions of great generality, which can be applied to fully discontinuous trial and test functions, simultaneously. This is in contrast with standard theory of distributions, which can be applied to discontinuous trial functions, only if test functions satisfy a corresponding degree of regularity, or viceversa. This paper is devoted to make a brief presentation of such extensions.
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