5 Matching Annotations
  1. Oct 2022
    1. 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

    2. method of approximation
      1. finding ci such that the difference u−f, measured in some norm, is minimized
      2. find u such that the error u−f is orthogonal to the space where we seek u
    1. 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

    2. integration by parts, boundary conditions, and coordinate mappings

      Core topics in FEM

    3. 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