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Weak form and strong form may refer to: Weaker and stronger versions of a hypothesis, theorem or physical law; Weak formulations and strong formulations of differential equations in mathematics; Differing pronunciations of words depending on emphasis; see Weak and strong forms in English; Weak and strong pronouns
Stress is a prominent feature of the English language, both at the level of the word (lexical stress) and at the level of the phrase or sentence (prosodic stress).Absence of stress on a syllable, or on a word in some cases, is frequently associated in English with vowel reduction – many such syllables are pronounced with a centralized vowel or with certain other vowels that are described as ...
In a weak formulation, equations or conditions are no longer required to hold absolutely (and this is not even well defined) and has instead weak solutions only with respect to certain "test vectors" or "test functions". In a strong formulation, the solution space is constructed such that these equations or conditions are already fulfilled.
Weakened weak form (or W2 form) [1] is used in the formulation of general numerical methods based on meshfree methods and/or finite element method settings. These numerical methods are applicable to solid mechanics as well as fluid dynamics problems.
Accordingly, the necessary condition of extremum (functional derivative equal zero) appears in a weak formulation (variational form) integrated with an arbitrary function δf. The fundamental lemma of the calculus of variations is typically used to transform this weak formulation into the strong formulation ( differential equation ), free of ...
Let us distinguish between a strong and a weak version." [53]:8-9 In either a stronger or a weaker form, the theory would limit Congress's power to divest the president of control of the executive branch. The hypothetical "strongly unitary" theory posits stricter limits on Congress than the "weakly unitary" theory.
Also, if u is differentiable in the conventional sense then its weak derivative is identical (in the sense given above) to its conventional (strong) derivative. Thus the weak derivative is a generalization of the strong one. Furthermore, the classical rules for derivatives of sums and products of functions also hold for the weak derivative.
Ritz–Galerkin method (after Walther Ritz) typically assumes symmetric and positive definite bilinear form in the weak formulation, where the differential equation for a physical system can be formulated via minimization of a quadratic function representing the system energy and the approximate solution is a linear combination of the given set ...