Partial differential equations | Numerical differential equations

Weak formulation

Weak formulations are important tools for the analysis of mathematical equations that permit the transfer of concepts of linear algebra to solve problems in other fields such as partial differential equations. 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. The Lax–Milgram theorem, named after Peter Lax and Arthur Milgram who proved it in 1954, provides weak formulations for certain systems on Hilbert spaces. (Wikipedia).

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Arthur Milgram | Cauchy–Schwarz inequality | Linear algebra | Babuška–Lax–Milgram theorem | Derivative | Differentiable function | Sobolev space | Coercive function | Banach space | Boundary (topology) | Green's identities | Poincaré inequality | Equation | Function (mathematics) | Dual space | Weak derivative | Bilinear form | Weak solution | Hilbert space | Lions–Lax–Milgram theorem | Complex number | Integration by parts | Poisson's equation | Matrix (mathematics) | Partial differential equation