Lectures related to Groundwater Flow: Laplace Equation and Boundary Conditions

Explains the numerical resolution of groundwater flows using finite differences and demonstrates the method with Excel.

Computational Geomechanics: Unconfined Flow

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

Boundary Conditions in Harmonic Functions

Explains harmonic functions and their boundary conditions, including Dirichlet and Robin conditions.

Computational Geomechanics: Unconfined Flow Analysis

Explores unconfined flow analysis in geomechanics, emphasizing iterative solution methods and boundary condition considerations.

Numerical Groundwater Flow Resolution: Finite Elements

Covers the numerical resolution of groundwater flows using finite elements and emphasizes the importance of spatial and temporal discretization.

Uniqueness Results for Poisson Equation

Explores uniqueness results for the Poisson equation and harmonic functions with different boundary conditions.

Finite Difference Grids

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

Linear PDEs of Order 2

Covers linear PDEs of order 2, focusing on elliptic second-order PDEs and boundary conditions.

Electrostatics and Green's Functions: Mathematical Methods

Discusses electrostatics, Green's functions, and the application of complex analysis in deriving potentials.

Rayleigh Taylor: Normal Mode Expansion

Explores normal mode expansion, Laplace equation solution, and dispersion relation analysis in Rayleigh Taylor instability.

Internal Heat Transfer Effects

Covers internal heat transfer effects in heterogeneous reactions, emphasizing dimensionless numbers and transport effects.

Finite Element Analysis: Advanced Mechanisms in Engineering

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

Laplace Equation in Polar Coordinates

Explores the Laplace equation in polar coordinates and its solution process through separation of variables.

Boundary Conditions and Basis Decomposition

Explores boundary conditions, basis functions, and PDE solutions using Fourier and Bessel series.

Modeling Water Transfers with Richards Equation

Discusses modeling water transfers with the Richards equation, including soil hydraulic functions, numerical methods, boundary conditions, and irrigation impact.

Laplace Equation in a Rectangle

Explores the Laplace equation in a rectangle using the separation of variables method.

Poincaré - Friedrichs: Theorem and Kernel Inequality

Explores the Poincaré - Friedrichs theorem and kernel inequality in constant conditions and boundary uniqueness.

Rectangular Waveguides: TE and TM Modes

Covers guided propagation in rectangular waveguides for TE and TM modes.

Electric Displacement in Dielectrics: Gauss's Law and Boundary Conditions

Introduces the concept of electric displacement vector D and explores boundary conditions in dielectrics.

Structural Mechanics Part 2: FEM & Scaling Laws

Explores Finite Element Modeling in Structural Mechanics, covering convergence, nonlinear displacement, and scaling laws in micro and nanosystems.