Lecture Note III: Least-Squares Method
نویسنده
چکیده
where L = (Lij)m×n is a block m×n matrix differential operator of at most first order, B = (Bij)l×n is a block l × n matrix operator, U = (Ui)n×1 is unknown, F = (Fi)m×1 is a given block vector-valued function defined in Ω, G = (Gi)l×1 is a given block vector-valued function defined on ∂Ω. Assume that first-order system (1.1) has a unique solution U . Boundary conditions in a least-squares formulation can be imposed either strongly (in the solution space) or weakly (by adding boundary functionals). For simplicity of presentation, we impose them in the solution space Φ. Assume that Φ is appropriately chosen so that least-squares functional is well defined. Define the least-squares functional by
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