Two-Scale FEMs for Non-Variational Elliptic PDEs
Explore advanced finite element methods for non-variational elliptic PDEs, focusing on two-scale approaches, monotonicity enforcement, and novel error estimation techniques for complex mathematical problems.
Larry Guth- Decoupling Estimates in Fourier Analysis
Explore recent developments in decoupling, a Fourier analysis technique with applications in harmonic analysis, PDE, and number theory. Survey key applications and proof concepts.
The Extraordinary Theorems of John Nash
Explore John Nash's revolutionary contributions to game theory and geometric analysis with Fields Medal winner Cédric Villani, delving into the world of mathematical genius and groundbreaking theorems.
The Divergence Theorem for Vector Fields - Applications and Generalizations
Explore the divergence theorem's applications in PDEs, geometry, physics, and engineering, including proofs of Archimedean principle and multidimensional Pythagorean theorem.
Implementation of Hybridizable Discontinuous Galerkin Methods - MFEM Workshop 2023
Explore advancements in hybridizable discontinuous Galerkin methods for high-order finite element calculations, featuring flexible implementations for diverse PDEs and applications.
Level Set Shape Optimization on Aggregated Polytopic Meshes
Explore level set shape optimization using polytopic meshes and Discontinuous Galerkin methods for improved boundary tracking and computational efficiency in structural optimization.
Convergent Evolving Surface Finite Element Algorithms for Geometric Evolution Equations
Explore convergent evolving surface finite element algorithms for geometric evolution equations, presented by Prof. Christian Lubich from University of Tübingen.
2D Finite Element Method - Radiation Boundary Condition
Explore radiation boundary conditions in 2D finite element methods. Learn key concepts and applications for advanced numerical analysis in electromagnetic simulations.
Introduction to the Finite Element Method - Basic Framework of FEM
Explore the fundamental concepts and framework of the Finite Element Method (FEM) in this introductory video lecture.
1D Finite Element Method: Wave Equation Basis and Testing Functions - Lecture 1
Explore basis and testing functions for 1D Finite Element Method in solving the 1D Wave Equation, enhancing understanding of numerical methods in computational physics.
Introduction to the Finite Element Method: 1D Basis Functions
Explore 1D basis functions in finite element method. Learn key concepts and applications for numerical analysis and engineering problem-solving.
1D Finite Element Method - 1D Wave Equation: Boundary Conditions
Explore boundary conditions for 1D wave equation using finite element method. Gain insights into solving complex mathematical problems in engineering and physics.
2D Finite Element Method: Shape Functions for 2D FEM
Explore 2D FEM shape functions in finite element analysis. Learn key concepts and applications for solving complex engineering problems.
1D Finite Element Method: Weak Form of 1D-FEM - Part 2
Explore advanced concepts of the weak form in 1D Finite Element Method, building on previous knowledge to deepen understanding of this numerical analysis technique.
1D Finite Element Method: Weak Form of 1D-FEM - Part 1
Explore the weak form of 1D Finite Element Method in this concise tutorial, focusing on fundamental concepts and practical applications in numerical analysis.
Introduction to the Finite Element Method: 2D Basis Functions
Explore 2D basis functions in finite element method. Learn key concepts and applications for advanced numerical analysis and engineering problem-solving.
2D Finite Element Method - Summary of FEM Procedure
Explore the 2D Finite Element Method procedure, covering key steps and applications in engineering analysis. Gain insights into this powerful numerical technique for solving complex problems.
1D Finite Element Method: Matrix Assembly for 1D Wave Equation
Explore matrix assembly techniques for the 1D Finite Element Method applied to the 1D Wave Equation, enhancing understanding of numerical solutions in computational physics.
High-Performance Implementations for High-Order Finite-Element Discretizations of PDEs
Explore matrix-free finite-element algorithms for solving PDEs, focusing on high-performance implementations and recent developments in performance engineering for complex geometries.
Hilbert-Space Valued LQ Mean Field Games - An Infinite-Dimensional Analysis
Explore infinite-dimensional analysis of Hilbert-space valued LQ mean field games, delving into advanced mathematical concepts and their applications in finance.
Numerical Solvers for Viscous Contact Problems in Glaciology
Explore numerical solvers for viscous contact problems in glaciology, focusing on ice flow modeling, subglacial cavities, and marine ice sheet dynamics. Overcome computational challenges in Stokes equations.