Lectures related to Boundary value problem

Finite Difference Grids

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

Internal Heat Transfer Effects

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

Poincaré - Friedrichs: Theorem and Kernel Inequality

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

Computational Geomechanics: Unconfined Flow

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

Boundary Conditions and Basis Decomposition

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

Regularity in Higher Dimension

Explores regularity in higher dimensions for scalar problems and discusses weak sense solutions and interior regularity.

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.

Finite Difference Method: Approximating Derivatives and Equations

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

Recent Advances in the Dimer Model and Its Applications

Covers recent advancements in the dimer model, emphasizing its applications in probability and conformal field theory.

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

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

Boundary Conditions - 1D Systems

Covers boundary conditions for heat diffusion in 1D systems.

Thermal Diffusion: Conservation and Fourier Law

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

Square Potential Well

Covers the concept of a square potential well and the search for solutions using trigonometric functions.

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.

Heterogeneous Reactions: Transport Effects

Explores transport effects in heterogeneous catalysis, including molecular diffusion and Knudsen diffusion in different types of pores.

Heat Transfer Applications

Explores the applications of the Fourier equation in heat transfer phenomena.

Translation Groups on [0,1]

Covers the study of translation groups on the interval [0,1] with different phases and the Riesz representation theorem on Hilbert space.

Mechanics of Kirchhoff Rods II

Explores the mechanics of Kirchhoff rods, focusing on 3D kinematics and twisted solutions.

Equilibrium in Tension: Verification and Compatibility

Covers the verification of equilibrium equations and compatibility in tension scenarios, ensuring uniform stress distribution.

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.