5 Matching Annotations
 Oct 2022

hplgit.github.io hplgit.github.io

minimizing e2e2\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

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


hplgit.github.io hplgit.github.io

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

integration by parts, boundary conditions, and coordinate mappings
Core topics in FEM

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
