1/5: Introduction, Stokes and Navier-Stokes Equations
1/7: Discretization of the Navier-Stokes Equations
1/9: Marker-and-Cell (MAC) discretization
1/12: Discretization matrices
1/14: Pressure-Correction methods
1/16: Direct versus Iterative Methods
1/19: Jacobi and Gauss-Seidel
1/21: Incomplete Factorizations, HW1 distributed, navierstokes.m
1/23: Polynomial Methods
1/26: Arnoldi Algorithm and GMRES
1/28: Lanczos and Conjugate Gradient
1/30: Cost of CG; analyzing Jacobi
2/2: Coarse-grid correction, two-grid algorithm
2/4: Multigrid and the V-cycle, HW1 due
2/6: Multigrid cycling
2/9: How effective is Multigrid?
2/11: Preconditioning
2/13: Midterm Exam
2/16: No class: Winter Semester Break
2/18: No class: Winter Semester Break
2/20: Elliptic PDEs and weak forms, HW2 distributed, fivept.m
2/23: Ritz-Galerkin approximation and error-estimates
2/25: Linear finite elements on [0,1]
2/27: Error estimates and element matrices
3/2: Function spaces and norms, Project proposals due
3/4: Lp and Sobolev spaces
3/6: Hilbert Spaces, Dual Spaces, and Riesz Representation, HW2 Due
3/9: Riesz Representation, Coercivity and continuity
3/11: Lax-Milgram and Céa's Lemmas
3/13: Poincaré-Friedrichs Inequality, element choice
3/16: SNOW DAY
3/18: Approximation properties; non-elliptic problems, HW3 distributed
3/20: Least-Squares finite elements
3/23: No class
3/25: No class
3/27: Finite elements for H(div) and H(curl)
3/30: Finite elements for the Stokes Equations
4/1: Final Exam
4/1: Final Project presentations
4/2: Written Final Project Reports due, HW3 Due
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