minimizing ||e||2||e||2||\boldsymbol{e}||^2 implies that ee\boldsymbol{e} is orthogonal to any vector vv\boldsymbol{v} in the space VVV
orthogonal to space vector to minimize
5 Matching Annotations
- Oct 2022
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hplgit.github.io hplgit.github.io
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method of approximation
- finding ci such that the difference u−f, measured in some norm, is minimized
- find u such that the error u−f is orthogonal to the space where we seek u
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hplgit.github.io hplgit.github.io
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Three types of approximation principles are covered: 1) the least squares method, 2) the L2L2L_2 projection or Galerkin method, and 3) interpolation or collocation.
approximation=? interpolation
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integration by parts, boundary conditions, and coordinate mappings
Core topics in FEM
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where ψi(x)ψi(x){\psi}_i(x) are prescribed functions and c0,…,cNc0,…,cNc_0,\ldots,c_N are unknown coefficients to be determined
actually Cn is the unknow function. but it's in a discritized form by point value
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