Finite Element Methods

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Related lectures (29)

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Numerical Methods: Euler and Crank-Nicolson

Covers Euler and Crank-Nicolson methods for solving differential equations.

Optimal Transport: Gradient Flows in Rd

Explores optimal transport and gradient flows in Rd, emphasizing convergence and the role of Lipschitz and Picard-Lindelöf theorems.

System of ODEs

Explores numerical methods for solving ODE systems, stability regions, and absolute stability importance.

Variational Formulation: Finite Element Method

Discusses the variational formulation of the heat equation using the finite element method.

Runge Kutta and Multistep Methods

Explores Runge Kutta and multistep methods for solving ODEs, including Backward Euler and Crank-Nicolson.

Zero-stability and absolute-stability

Explores zero-stability and absolute-stability in numerical methods, including Forward Euler, Backward Euler, Crank-Nicolson, and Heun's methods.

Euler Backward Method: ODEs

Explores the Euler backward method for ODEs, discussing stability, error reduction, and implicit vs explicit methods.

Explicit Stabilised Methods: Stochastic Differential Equations

Covers explicit stabilized methods for stiff stochastic differential equations, analyzing their properties and applications.

Error Estimation in Numerical Methods

Explores error estimation in numerical methods for solving ordinary differential equations, emphasizing the impact of errors on solution accuracy and stability.

Runge-Kutta Methods

Explains the Runge-Kutta methods, particularly the explicit scheme of order 4 (ERK4), and how to optimize parameters for accuracy.