Abstract
This chapter reviews the classical tools for the construction of variational formulations of boundary value problems and the corresponding discretization. It also introduces the basic boundary value problem in a bounded medium, and its strong solution, and provides a method for constructing a variational formulation of the boundary value problem using the test function (weighted function) method. The chapter also defines the admissible function space of the problem and uses Green's formula. It also explains a weak solution of the boundary value problem, which corresponds to the solution of the variational formulation, and reviews the Ritz‑Galerkin and finite element methods, which constitute the basic tools.
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