School of Mathematics and Computing Sciences, Chalmers University of Technology and Goteborg University
School of Mathematics and Computing
Sciences,
Chalmers University of
Technology
and
Goteborg University
Theorem 5.3; The interpolation error (proof either as in the CDE or in the Lecture Notes).
Equivalences: Show (in the 1D case) that the boundary value problem for the stationary heat equation is equivalent to a corresponding variational formulation and a minimization problem (page 178-182 CDE).
Theorem 8.1; a priori error estimate for the 2 point boundary value problems, (the complete proof is given in Theorems 8.1, 8.2 and 8.3 in Lecture Notes).
Theorem 8.2; a posteriori error estimate for the 2 point boundary value problems, (the proof is given through the arguments leading to Theorem 8.4 in the Lecture Notes).
Lemma 9.1; stability estimates for the dual of a general initial value problem, (a detailrd proof can be found "inside the proof of Theorem 9.2" in the Lecture Notes).
Theorem 9.2; a posteriori error estimates for cG(1), for a general initial value problem.
Theorem 9.4; a priori error estimates for dG(0), for a general initial value problem, (a detailed proof can be found in Lecture Notes).
Theorem 21.1; the Lax-Milgram Theorem.
Theorem 15.4; a posteriori error estimates for the Poisson's equation.
Lemma 16.1; Stability estimates for the heat equation.