Lectures related to Finite Element Modeling: Systematization

Finite Element Modeling: Systematization and Construction

Covers the systematization and construction of a 2D finite element model.

Geometrical Aspects of Differential Operators

Explores differential operators, regular curves, norms, and injective functions, addressing questions on curves' properties, norms, simplicity, and injectivity.

Regular Curves: Parametrization and Tangent Vectors

Explores regular curves, examples like segments and functions, and curvilinear integrals along regular curves.

Finite Element Method: Construction and Integration

Explores the construction of a 2D finite element model and the treatment of curvilinear integrals.

Vector Fields Analysis

Explores vector fields analysis, covering curvilinear integrals, potential fields, and field connectivity conditions.

Finite Element Method: Global vs Local Approach

Compares the global and local approaches of the Finite Element Method.

Curvilinear Integrals

Covers curvilinear integrals in R^n, focusing on continuous functions and curves.

Curvilinear Integrals: Tangent Vectors and Oriented Arcs

Explains the tangent vectors and curvilinear integrals along oriented arcs.

Green-Riemann Formula: Curvilinear Integrals

Covers the Green-Riemann formula, connectedness by arcs, parametrization of curves, and open simply connected domains in the Oxy plane.

Curvilinear Integrals

Covers the calculation of curvilinear integrals for a continuous function in R^n and the interpretation of the integral as the sum of small segments along a curve.

Surface Integrals: Parameterization and Regularity

Explains surface integrals, parameterization, and regularity of surfaces.

Total Differential: Definition and Integrals

Explores the definition of total differential and its applications in integral calculus.

Curvilinear Integrals: Interpretation and Convexity

Explores the interpretation of curvilinear integrals in vector fields and the proof of potential fields.

Finite Element Method: Local Approach

Explores the local approach of the finite element method, covering nodal shape functions, solution restrictions, sizes, boundary conditions, and assembly operations.

Curvilinear Integrals and Green's Theorem

Introduces curvilinear integrals, parameterization, and Green's Theorem for conservative fields.

Differential Forms Integration

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

Tangent and Normal Vectors: Curves in R^2

Covers the parameterization of curves, tangent and normal vectors, simple closed curves, exterior normal, regular curves, and domains in R^2.

Fields from Potential: Derivation and Curvilinear Integral

Explores deriving fields from a potential, curvilinear integrals, and necessary conditions for domains.

Green's Theorem: Transforming Integrals in 2D

Covers Green's Theorem, transforming 2D integrals into 1D line integrals.

Surface Integrals: Regular Parametrization

Covers surface integrals with a focus on regular parametrization and the importance of understanding the normal vector.