Heat Equation in 1D: Chapter 12

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

Explores the basics of heat conduction in solids, covering Fourier's law, thermal conductivity, energy conservation, and practical applications.

Covers numerical methods for solving boundary value problems using Crank-Nicolson and FFT.

Explores the numerical simulation of steady convection-diffusion problems, discretization, boundary conditions, and algebraic system assembly.

Explores the Fourier equation in 2D for a stationary regime without heat production in a semi-infinite wall.

Explains conservation of energy and Fourier's law in thermal diffusion.

Explores the parabolic heat equation evolution and numerical solution methods.

Explores inverse monotonicity in numerical methods for differential equations, emphasizing stability and convergence criteria.

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

Covers modeling and numerical schemes for diffusion-convection problems.