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Finite Element Method & Applications in Design MENG 4553, Youssef…
Finite Element Method & Applications in Design MENG 4553
Modeling Physical Systems via PDEs
Model Linear PDEs
Weak Formulation of PDES (BVPs)
Vector Spaces
Sobolev
Hilbert
Boundary Conditions
Dirichlet
Neumann
Weakform in Finite Dimension
Projection Theorem
Galerkin's Theorem
Finite Element Method Basics
Piecewise Polynomials as Solutions
Interpolation
Basic Functions
Mesh Data Structures
Node
Element
Connectivity
Programming FEM for Problem Solving (MATLAB)
Programming Simple BVP
Assembly of System Equations
Boundary Conditions Implementation
Programming General BVP
Anisotropic Scalar BVP
Isotropic Elasticity
Mesh Locking
Solvers for FEM
Direct Solvers for FEM
The Cholesky Factorization
Iterative Solvers for FEM
Steepest Descent Method
Conjugate Gradient Method
Adaptive Meshing and Error Analysis
Adaptive Meshing (Error-based)
Error Estimators
Error Indicators
Youssef Hermina
900193482