MATH688 FINITE ELEMENT SOL. OF DIFF. EQUATIONS
| Course Code: | 2360688 |
| METU Credit (Theoretical-Laboratory hours/week): | 3 (3.00 - 0.00) |
| ECTS Credit: | 8.0 |
| Department: | Mathematics |
| Language of Instruction: | English |
| Level of Study: | Graduate |
| Course Coordinator: | Prof.Dr. CANAN BOZKAYA |
| Offered Semester: | Fall Semesters. |
Course Objectives
At the end of this course, the student will:
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acquire a solid foundation in the calculus of variations and weighted residual methods as a basis for finite element analysis
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understand the theory, construction, and implementation of interpolation (shape) functions, including higher-order elements
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develop finite element formulations for linear and nonlinear ordinary differential equations, with applications to continuum mechanics
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formulate and solve time-dependent problems using finite element techniques
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perform error estimation, convergence analysis, and numerical implementation of the finite element method in steady and transient problems
Course Content
Calculus of variations. Weighted residual methods. Theory and derivation of interpolation functions. Higher order elements. Assembly procedure, insertion of boundary conditions. Finite element formulation of ordinary differential equations, some applications. Error and convergence analysis. Finite element formulation of non-linear differential equations. Time dependent problems. Convergence and error analysis. Solution of the resulting algebraic system of equations. Applications on steady and time dependent problems in applied continuum mechanics.
Course Learning Outcomes
Student, who passed the course satisfactorily will be able to:
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apply the calculus of variations and weighted residual methods in the derivation of finite element formulations
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derive and construct interpolation functions, including those for higher-order elements
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implement the element-level assembly procedure and impose essential and natural boundary conditions
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formulate and solve finite element models for linear and nonlinear ordinary differential equations
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develop time-stepping algorithms for transient problems within the finite element framework
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analyze convergence, stability, and error behavior of finite element solutions
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solve algebraic systems arising from FEM discretizations using appropriate numerical methods
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apply finite element methods to practical problems in applied continuum mechanics, including both steady-state and time-dependent cases
Program Outcomes Matrix
| Level of Contribution | |||||
| # | Program Outcomes | 0 | 1 | 2 | 3 |
| 1 | Acquires mathematical thinking skills (problem solving, generating ways of thinking, forming correspondence, generalizing etc.) and can use them in related fields. | ✔ | |||
| 2 | Gains academic maturity through self-study. | ✔ | |||
| 3 | Can design mathematics related problems, devise solution methods and apply them when appropriate. | ✔ | |||
| 4 | Carries out parts of a mathematical research program independently. | ✔ | |||
| 5 | Has a command of Turkish and English languages so that he/she can actively communicate (read, write, listen and speak). | ✔ | |||
| 6 | Contributes to solving global, environmental and social problems either individually or as being part of a social group. | ✔ | |||
| 7 | Respects ethical values and rules; applies them in professional and social issues. | ✔ | |||
| 8 | Can work cooperatively in a team and also individually. | ✔ | |||
| 9 | Gets exposed to academic culture through interaction with others. | ✔ | |||
| 10 | Comprehends necessity of knowledge, can define it and acquires it; uses knowledge effectively and shares it with others. | ✔ | |||
0: No Contribution 1: Little Contribution 2: Partial Contribution 3: Full Contribution