Learn · Computational Fluid Dynamics using the Finite Element Method
Lecture 38 of 45Week 11
Lecture 38: Convergence of Generalized Trapezoidal Method
Prof. Sanjay Mittal · IIT Kanpur
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- Computational Fluid Dynamics using the Finite Element Method, IIT Kanpur (at NPTEL)
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All the lectures
- Lecture 1 : Introduction to CFD & HPC
- Lecture 2 : Overview of the course: Finite Element Methods for Fluid Dynamics
- Lecture 3 : Simple Finite Difference Methods to solve ODEs
- Lecture 4 : Simple Finite Difference Methods to solve PDEs (Part - A)
- Lecture 5 : Simple Finite Difference Methods to solve PDEs (Part -B)
- Lecture 6 : Vector Spaces, basis, completeness (Part -A)
- Lecture 7 : Vector Spaces, basis, completeness (Part- B)
- Lecture 8 : Continuity, Differentiability and Smoothness (Part - A)
- Lecture 9 : Continuity, Differentiability and Smoothness (Part - B)
- Lecture 10 : Method of Weighted Residual
- Lecture 11 : Weak form of a Steady, 1D problem (Part - A)
- Lecture 12 : Weak form of a Steady, 1D problem (Part - B)
- Lecture 13 : Galerkin's Approximation and Matrix form (Part - A)
- Lecture 14 : Galerkin's Approximation and Matrix form (Part - B)
- Lecture 15 : Example to illustrate Galerkin's approximation (Part - A)
- Lecture 16 : Example to illustrate Galerkin's approximation (Part - B)
- Lecture 17: Piecewise Linear Finite Element Space: Element Level Matrices and Vectors (Part -A)
- Lecture 18: Piecewise Linear Finite Element Space: Element Level Matrices and Vectors (Part - B)
- Lecture 19: Assembly of Element Level Matrices and Vectors ( Part - A)
- Lecture 20: Assembly of Element Level Matrices and Vectors ( Part - B)
- Lecture 21: Strong, Weak, and Galerkin forms of Two- and Three-Dimensional problems (Part - A)
- Lecture 22: Strong, Weak, and Galerkin forms of Two- and Three-Dimensional problems (Part - B)
- Lecture 23: Matrix form of Two- and Three-Dimensional Problems (Part - A)
- Lecture 24: Matrix form of Two- and Three-Dimensional Problems (Part - B)
- Lecture 25: Assembly of element-level matrices and vectors for Two- and Three-Dimensional problems (Part - A)
- Lecture 26: Assembly of element-level matrices and vectors for Two- and Three-Dimensional problems (Part - B)
- Lecture 27: Classical Linear Electrostatics: vector unknown (Part - A)
- Lecture 28: Classical Linear Electrostatics: vector unknown (Part - B)
- Lecture 29: Finite Element Interpolation/ Basis Functions (Part - A)
- Lecture 30: Finite Element Interpolation/ Basis Functions (Part - B)
- Lecture 31: Numerical Integration, Derivatives of shape function (Part - A)
- Lecture 32: Numerical Integration, Derivatives of shape function (Part - B)
- Lecture 33: Introduction to time-dependent problems (Part - A)
- Lecture 34: Introduction to time-dependent problems (Part - B)
- Lecture 35: 1D Unsteady Linear Heat Conduction; Generalized Trapezoidal Method (Part - A)
- Lecture 36: 1D Unsteady Linear Heat Conduction; Generalized Trapezoidal Method (Part - B)
- Lecture 37: Stability Analysis of Time Integration Methods
- Lecture 38: Convergence of Generalized Trapezoidal Method
- Lecture 39: Methods for non-linear problems
- Lecture 40 : Numerical instability in the Galerkin Formulation for Advection Dominated Flows (Part - A)
- Lecture 41 : Numerical instability in the Galerkin Formulation for Advection Dominated Flows (Part - B)
- Lecture 42 : SUPG (Streamline-Upwind/Petrov-Galerkin) Method for Advection dominated flows (Part - A)
- Lecture 43 : SUPG (Streamline-Upwind/Petrov-Galerkin) Method for Advection dominated flows (Part - B)
- Lecture 44 : Stabilized Finite Element Formulations for Flows (Part - A)
- Lecture 45 : Stabilized Finite Element Formulations for Flows (Part - B)