1. Simpson's rule is three-diagonal
2. For the standard linear basis is the smallest possible
functions, the degrees of freedom (dofs)
3. The 2nd law of Thermodynamics states that is made smaller
the entropy of an isolated macroscopic system
4. The Finite element method is an orthogonal basis for
L^2(0,2*pi)
5. Forming a projection into a subspace of is unique
functions
6. Trapezoidal rule is constant
7. Linear hat-functions and exact is equal to the required
integration implies that the number of degrees of freedoms
mass-matrix (dofs)
8. A finer computational mesh generally, is non-decreasing
but not always, implies that the error
9. The Legendre polynomials is dependent on the regularity
of the target function
10. Generally, whatever basis is used, is not the same thing
a mass-matrix
11. The Laws of Thermodynamics imply that is mathematically equivalent
the energy in a closed system to the Lagrange interpolant,
but is numerically preferred
12. The Finite difference method is diagonal
13. For a well-posed problem, the solution is a matter of defining
suitable basis functions and
forcing the residual to be
orthogonal against all such
basis functions
14. The family of trigonometric functions sin(m*x) is exact for quadratic
and cos(n*x), for m = 1,2,3,... and n = 0,1,2,3... polynomials
15. Standard linear hat-functions plus the is an orthogonal polynomial
trapezoidal rule implies that the mass-matrix basis for L^2(-1,1)
16. The dimensionality of a discrete is obtained by integrating
function space a linear interpolant
17. Orthogonal basis functions implies that is always symmetric
the mass-matrix
18. Beware that order of convergence and is diagonal
accuracy
19. When measured in the L^2-norm, the error is a kind of "PDE-solver
in the projected result through interpolation"
20. The error in an interpolant is just the function's
nodal-values
21. The Newton interpolating polynomial is a projection-based
PDE-solving numerical method