Lecture

Continuity and Galerkin Method

Related lectures (27)

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Linear Operators: Boundedness and Spaces

Explores linear operators, boundedness, and vector spaces with a focus on verifying bounded aspects.

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Explains finite difference grids for computing solutions of elastic membranes using Laplace's equation and numerical methods.

Finite Elements: Problem with Limits

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Explores boundary value problems, finite difference method, and Joule heating examples in 1D.

Finite Difference Method: Approximating Derivatives and Equations

Introduces the finite difference method for approximating derivatives and solving differential equations in practical applications.

Linear Statics of Deformable Solids

Introduces linear statics for linear elastic solids in small deformations, stress equilibrium, the Virtual Work Principle, and the Finite Element Method.

Numerical Methods for Boundary Value Problems

Covers numerical methods for solving boundary value problems using finite difference, FFT, and finite element methods.

Distributions and Derivatives

Covers distributions, derivatives, convergence, and continuity criteria in function spaces.

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Provides an overview of advanced mechanisms analysis using Finite Element Method and Finite Element Analysis in engineering applications.

Computational Geomechanics: Unconfined Flow

Explores unconfined flow in computational geomechanics, emphasizing weak form derivation and relative permeability.

Boundary Value Problems: Numerical Methods

Covers the motivation and examples of boundary value problems, the finite difference method, and the approximation of local derivatives.

Numerical Methods: Boundary Value Problems

Explores numerical methods for boundary value problems, including heat diffusion and fluid flow, using finite difference methods.

Computational Geomechanics: Week 4

Explores transient flow in porous media, covering governing equations, stability conditions, and numerical methods.

Quantum Mechanics: Mathematical Framework

Introduces the need for a mathematical framework to describe linear operators on infinite-dimensional Hilbert spaces in quantum mechanics.

Heat Equation in 1D: Chapter 12

Explores the heat equation in 1D, emphasizing conservation of thermal energy and numerical solution methods.

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Explores the explicit 2-level scheme for advection-diffusion and the convergence of digital solutions.

Consistency and Stability in Numerical Methods

Explores consistency and stability in numerical methods, emphasizing error analysis and the role of boundary conditions.

Lecture 4: Hilbert Spaces and Unique Solutions

Covers Hilbert spaces and unique solutions in function spaces, emphasizing the Lax-Milgram theorem.