Melanin 发表于 2025-3-21 18:34:19
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https://doi.org/10.1007/978-3-322-89674-2 the screen. The nature of the Green’s functions, their intricacies and approximability, their relevance for modelling the mechanics in a problem are discussed at length in this introductory chapter which closes with instructions on how to calculate influence functions with an FE-program.CLAIM 发表于 2025-3-22 14:53:03
https://doi.org/10.1007/978-3-642-79905-1context, theoretically and practically. Most functionals are unbounded and so the FE-method, strictly speaking, transgresses the bounds of the theory but it does so very successfully.The analogy between Green’s functions and Lagrange multipliers finally provides estimates for nonlinear problems at the linearization point.CLAIM 发表于 2025-3-22 19:10:33
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,Finite Elements and Green’s Functions, The special nature of the FE-solution allows to extend Betti’s Theorem (p.,u.) = (p.,u.) to the FE-solutions in the following sense (p.,u..,p.,u..) which establishes that the FE-solution is the scalar product of the approximate Green’s function G. and the original right-hand side p, namely u. = (G.handle 发表于 2025-3-23 09:25:43
The Discretization Error, the energy error in powers of the mesh-width h. In goal-oriented refinement where the focus is on minimizing the error in certain functionals the adaptive refinement is steered by two errors, the error in the primal, the original, problem and the error in the dual problem, the approximation of the