ECTS credits ECTS credits: 3
ECTS Hours Rules/Memories Student's work ECTS: 51 Hours of tutorials: 3 Expository Class: 9 Interactive Classroom: 12 Total: 75
Use languages Spanish, Galician
Type: Ordinary subject Master’s Degree RD 1393/2007 - 822/2021
Departments: Applied Mathematics
Areas: Applied Mathematics
Center Faculty of Mathematics
Call: Second Semester
Teaching: With teaching
Enrolment: Enrollable | 1st year (Yes)
Complete the training of students in the finite element method for partial differential equations, addressing in some depth the following aspects:
i) theoretical and practical foundations of Lagrange finite elements for boundary value problems in dimension 2 and 3, including the basis for programming it in a high-level language.
ii) Introduction to finite element methods for other problems: fourth order (Hermite), evolutionary and mixed.
1. Approximation of elliptic problems Abstract: Lax-Milgram Lemma, Lemma of Cea.
2. Approximation of elliptic problems of order 2 in dimension 2 and 3 with Lagrange finite elements (triangles, tetrahedra, quadrilaterals and hexahedral): description and construction of finite element spaces, references, basic functions, affine equivalence.
3. A priori error estimates for afin equivalent families of finite element method: quality of meshes, convergence, regular families. Case of curved domains.
4. Computer programming method: elementary matrices and second members, quadrature, assembly, storage profile, boundary conditions. Applications to flexion of membranes, heat conduction, two-and three-dimensional elasticity.
5. Evolution parabolic problem and hyperbolic of order 2 in time: variational formulation, discretization in space and time.
6. Finite elements for fourth order problems: bending of elastic beam, elastic plate bending.
7. Introduction to mixed problems: Stokes equation. Existence and uniqueness of solution of the abstract formulation: inf-sup condition.
8. Mixed finite elements: numerical resolution of Stokes equation. A priori error estimates. Discrete inf-sup condition.
BASIC BIBLIOGRAPHY:
Bécache, E., Ciarlet, P. J., Hazard, C., Luneville, E., La méthode des éléments finis: de la théorie a la pratique. Tome II. Compléments., Les Cours, Les Presses de l’ENSTA, Paris, 2010.
Ciarlet, P.G., The finite element method for elliptic problems. North-Holland, 1978.
Ciarlet, P. J., Luneville, E., La méthode des éléments finis: de la théorie a la pratique. Tome I. Concepts généraux., Les Cours, Les Presses de l’ENSTA, Paris, 2009.
Krizek, M., Neittaanmaki, P., Finite element approximation of variational problems and applications. Longman Scientific&Technical, 1984.
Raviart, P.A., Thomas, J.M., Introduction à l’analyse numérique des équations aux derivées partielles. Masson. 1983.
COMPLEMENTARY BIBLIOGRAPHY:
Brenner, S.C., Scott, L.R., The mathematical theory of finite element methods. Springer - Verlag. 1994 (3ª ed., 2008).
Brezzi, F., Fortin, M., Mixed and hybrid finite element methods, vol. 15 of Springer Series in Computational Mathematics, Springer - Verlag, New York, 1991.
Ern, A., Guermond, J.L., Theory and Practice of finite elements. Springer - Verlag. 2004.
Girault, V., Raviart, P.A., Finite element methods for Navier - Stokes equations. Springer - Verlag. 1986.
Glowinski, R, Numerical methos for nonlinear variational problems. Springer. 1984.
Pironneau, O., Finite element methods for fluids. John Wiley - Masson. 1989.
Quarteroni, A., Numerical models for differential problems. Springer - Verlag. 2009 (2ª ed., 2014).
Quarteroni, A., Valli, A., Numerical approximation of Partial Differential Equations. Springer - Verlag. 1997.
Roberts, J.E., Thomas, J.M., Mixed and hybrid methods. Handbook of Numerical Analysis. Vol . II. North Holland. 1991.
Thomee, V., Galerkin finite element methods for parabolic problems. Springer - Verlag. 1997 (2ª ed., 2006).
Verfurth, R., A Review of A Posteriori Error Estimation and Adaptive Mesh - refinement Technique, Wiley & Teubner, 1996.
Basic skills that students should acquire during their studies (established by Royal Decree 861/2010)
General skills
CG3 Being able to integrate knowledge in order to state opinions using information that even incomplete or limited, include reflecting on social and ethical responsibilities linked to the application of their knowledge;
CG5 To have the appropriate learning skills to enable them to continue studying in a way that will be largely self-directed or autonomous, and also to be able to successfully undertake doctoral studies.
Specific skills
CE4: Being able to select a set of numerical techniques, languages and tools, appropriate to solve a mathematical model.
CS2: To adapt, modify and implement software tools for numerical simulation.
The course is developed through theoretical classes taught by videoconference, recorded and reproduced in streaming, backed by written material that is made available to students in the virtual course.
Each student will carry out a written and tutored work on the solution using the finite element method of a problem that includes from the theoretical formulation to the resolution using the existing software in the university systems to which they will have access, complemented by their own programs.
Face-to-face tutoring, through a virtual course, by email or by any audiovisual platform.
The CG3, CG5, CE4 and CS2 competences will be evaluated with the procedures indicated below.
In cases of fraudulent performance of exercises or tests, the provisions of the Regulations for the evaluation of the academic performance of students and the review of grades will apply.
The evaluation of the work done throughout the course will have a value of 80% of the final grade (8/10). An online presentation interview with the student may be required at the assessment to answer questions about the work itself.
The remaining 20% of the grade (2/10) will be obtained through an individual written or oral test on the theoretical content of the course. This test will be carried out remotely through the same videoconference as the classes.
There are two opportunities in each exam. Work and exam grades can be retained from first to second chance.
Any student who does not submit the work within the deadlines established for this purpose is considered "Not submitted".
Hours of teacher activity: 21 hours
-Teaching Expository: 15 hours
- Interactive Teaching: 6 hours
Student activities individually or in groups: 54 hours
- Exam Preparation: 9 hours
- Works: 40 hours
- Reviews: 5 hours
Total hours of student work: 75 hours
To have studied a basic course in finite elements and a course of partial differential equations and variational theory
Contingency plan for the adaptation of this guide to the document Bases for the development of a secure face-to-face teaching in the 2020-2021 academic year, approved by the USC Governing Council in its ordinary session held on 19 June 2020.
SCENARIO 1 (adapted normality)
Methodology
The course is developed through theoretical classes taught by videoconference, recorded and reproduced in streaming, supported by written material that is made available to students in the virtual course.
Each student will carry out a written tutored work on the resolution by the method of finite elements of a problem that includes from the theoretical formulation to the resolution using existing software in the systems of the universities put to his disposal, complemented with own programs.
Face-to-face tutoring, through a virtual course, by e-mail or by any audiovisual platform.
Evaluation:
The evaluation of the work done throughout the course will have a value of 80% of the final grade (8/10). An online interview with the student may be required in the assessment to clarify doubts about the work itself.
The remaining 20% of the grade (2/10) will be obtained by an individual written or oral test on the theoretical contents of the course. This test will be conducted remotely through the same videoconference as the classes.
There are two exam opportunities in each call. Job and exam grades can be retained from the first to the second opportunity.
Any student who does not submit the work within the deadlines set for this purpose is considered "Not Presented".
SCENARIO 2 (Spacing)
The methodology and assessment system would be the same as in scenario 1 as long as the number of students attending each videoconference classroom allowed the distances to be kept. This situation is not predictable given the number of students enrolled in recent years. In any case, the classes would always be recorded and would be available to students without the need for their presence in the classroom. If circumstances so advised, we could apply the guidelines in scenario 3. Tutoring through a virtual course, by e-mail or by any audiovisual platform.
SCENARIO 3 (Closure of facilities)
The methodology and assessment system would be the same as in scenarios 1 and 2 with the difference that classes, interviews and exam would be done from the MS Teams platform instead of video conferencing. We need to ensure that the computer programs they use for the assignments remain available to students. Tutoring through a virtual course, by e-mail or by any audiovisual platform.
Juan Manuel Viaño Rey
Coordinador/a- Department
- Applied Mathematics
- Area
- Applied Mathematics
- Phone
- 881813188
- juan.viano [at] usc.es
- Category
- Professor: University Professor
| Thursday | |||
|---|---|---|---|
| 09:00-11:00 | Grupo /CLE_01 | Spanish | Computer room 5 |
| Friday | |||
| 10:00-11:00 | Grupo /CLE_01 | Spanish | Computer room 5 |
| 05.27.2021 16:00-20:00 | Grupo /CLE_01 | Computer room 5 |
| 06.16.2021 10:00-14:00 | Grupo /CLE_01 | Computer room 5 |