Course Diary TMA 372 and MMG800, MVE 455, 2019

Latest news

There is a second round for Assigment 2 with the new deadline: March 27th.
There will be a "tentavisning", WED. April 10, 12-12:45 in Math department MVL 14.

Old exams (First 2 are the current exams of 2019/03)

2019: Exam AND Solutions for KF3, MVE455: tenta+sol_2019-0318(pdf),

2018: Exam AND Solutions for KF3, MVE455: tenta+sol_2018-0312(pdf),

2017: Exam AND Solutions: tenta+sol_2017-03-15(pdf),

2016: Exam AND Solutions for KF3: tenta+sol_2016-08-1(pdf),

2016: Exam AND Solutions for KF3: tenta+sol_2016-06-10(pdf),

2016: Exam AND Solutions for KF3: tenta+sol_2016-04-06(pdf),

2016: Exam AND Solutions: tenta+sol_2016-08-24(pdf),

2016: Exam AND Solutions: tenta+sol_2016-03-16(pdf),

2016: Exam AND Solutions for KF3: tenta+sol_2016-03-14(pdf),

2015: Exam AND Solutions: tenta_2015-06-09(pdf),

2015: Ordinary Exam AND Solutions: tenta_2015-03-18(pdf),

2014: Ordinary Exam AND Solutions: tenta_2014-03-12(pdf),

Below is the progress of the course so far:

• Study weak 1: I covered (basically) Chapters 1 and 3 (partially) and 4 from the book:
Galerkin approach for a 1D population daynamics
The phenomenon of ill-conditioning in polynomial approximation.
Approximated procedure by piecewise polynomials. (stationary heat conduction in 1D).
Stiffness matrix.

• Study weak 2: I covered chapters 5 and the theory parts of Chapters 7 and 3:
polynomial approx. Gauss quadrature rule. Lagrange interpolation.
Equvivalnce relations beteween BVP (boundary value problrem), VF (variational formulation) and MP (minimization problem).
A priori and A posteriori error estimates for stationay heat equation in the energy norm.

• Study weak 3: I covered major part of Chapter 8: Initial value problems (IVP)
Exact solution, stabilities, dual problem, cG(1) and dG(0) for IVP A posteriori error estimates for cG(1)
A posteriori error estimates for cG(1) abd dG(0). A priori error estimates for dG(0) for stationay heat equation

• Study weak 4: I covered Chapter 9: The Initial Boundary Value Problem.
Stanilty for the heat equation in ebery norm the cG81)-cG(1) approximation for both heat and wave equations.
Consevation law for the wave equation

• Study weak 5:
• Study weak 6:
• Study weak 7:

Put assignments in the folder box outside Maximilian office. No E-mail submission is accepted!
You may also hand in the solutions to homework assignments during the lecture.
Submit "only one" solution set of homework assignments for your group.
Write the names and id-number (personnummer) of gruop members on the first page.

Extra Support Material:

2. MATLAB Code Examples: poisson.m, poi2D.m

Sample Exam Questions:

At least one question on the final exam will be to prove one of the following theorems.

• Theorem 3.7: The Poincare inequality I & II.

• Theorem 3.11: Variational Formulation (VF) is equivalent to Minimization Problem (MP).

• Theorem 3.15: The Lax-Milgram Theorem (Riesz version): There is a unique solution to the abstract minimization problem (M).

• Theorem 5.1: Prove the interpolation error estimate (1) for q=1 and p=infinity.

• Theorems 7.1 and 7.2: A priori error estimates in energy norm.

• Theorem 7.3: A posteriori error estimates in energy norm.

• Theorem 8.2: Stabilty estimates for IVP.

• Theorem 8.5: dG(0) error estimate for IVP.

• Theorems 9.1 and 9.2: Stability estimates for the heat equation

• Theorems 9.5: The wave equation; Conservation of energy.

• Theorems 11.3: (Poisson) A priori error estimates for the gradient.

• Theorems 12.1: (Heat equation) Energy estimate.