Finite element method | Partial differential equations | Numerical differential equations
p-FEM or the p-version of the finite element method is a numerical method for solving partial differential equations. It is a discretization strategy in which the finite element mesh is fixed and the polynomial degrees of elements are increased such that the lowest polynomial degree, denoted by , approaches infinity. This is in contrast with the "h-version" or "h-FEM", a widely used discretization strategy, in which the polynomial degrees of elements are fixed and the mesh is refined such that the diameter of the largest element, denoted by approaches zero. It was demonstrated on the basis of a linear elastic fracture mechanics problem that sequences of finite element solutions based on the p-version converge faster than sequences based on the h-version by Szabó and in 1978. The theoretical foundations of the p-version were established in a paper published Babuška, Szabó and in 1981 where it was shown that for a large class of problems the asymptotic rate of convergence of the p-version in energy norm is at least twice that of the h-version, assuming that quasi-uniform meshes are used. Additional computational results and evidence of faster convergence of the p-version were presented by Babuška and Szabó in 1982. The distinction between the h- and p-versions exists primarily for historical and theoretical reasons. In practical applications the design of the mesh and the choice polynomial degrees are both important. In fact, it is possible to realize exponential rates of convergence when the p-version is used in combination with proper mesh design. This point was discussed from the engineering perspective by Szabó and from the theoretical perspective by and Babuška in 1986. Realization of exponential rates of convergence for Maxwell equations was discussed by , and in 2005 (Wikipedia).
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From playlist Pneumatic and Hydraulics
Some Prerequisit Analysis on the Pochhammer Symbol
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From playlist Number Theory
The Birds, Bees and the MEMES - Our Lord and Saviour -1/12 [ Math Snaccs #3 ]
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From playlist Integrals
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TabletClass Math: https://tcmathacademy.com/ Math help with the Pythagorean Theorem. For more math help to include math lessons, practice problems and math tutorials check out my full math help program at https://tcmathacademy.com/ Math Notes: Pre-Algebra Notes: https://tabletclass
From playlist GED Prep Videos
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From playlist Introduction to Pyhton for mathematical programming
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This video helps with the question: 'What is BIM'? http://www.nationalBIMlibrary.com is the construction industry's free-to-use resource of NBS standard BIM content. Objects are available in IFC, ArchiCAD, Bentley, Revit and Vectoworks format. NBS National BIM Library content links with
From playlist The World's Best BIM Videos | Curated by The B1M
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From playlist Introduction to Pyhton for mathematical programming
FEM@LLNL | Efficient Techniques for Fluid Structure Interaction
Sponsored by the MFEM project, the FEM@LLNL Seminar Series focuses on finite element research and applications talks of interest to the MFEM community. On July 26, 2022, Jeffrey Banks of Rensselaer Polytechnic Institute presented "Efficient Techniques for Fluid Structure Interaction: Comp
From playlist FEM@LLNL Seminar Series
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From playlist Introduction to Pyhton for mathematical programming
Gwenaelle Douaud, University of Oxford - Stanford Big Data 2015
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From playlist Big Data in Biomedicine Conference 2015
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The successful approach to solving Fermat's problem reflects a move in number theory from abelian to non-abelian arithmetic. This lecture was held by Abel Laurate Sir Andrew Wiles at The University of Oslo, May 25, 2016 and was part of the Abel Prize Lectures in connection with the Abel P
From playlist Sir Andrew J. Wiles
DIRECT 2021 12 Scientific Machine Learning
DIRECT Consortium at The University of Texas at Austin, working on novel methods and workflows in spatial, subsurface data analytics, geostatistics and machine learning. This is Applications of Scientific Machine Learning for Petroleum Engineering. Join the consortium for access to all
From playlist DIRECT Consortium, The University of Texas at Austin
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Project Page: http://www.cs.cmu.edu/~kmcrane/Projects/MonteCarloGeometryProcessing/index.html
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FEM@LLNL | The Shifted Boundary Method: An Immersed Approach for Computational Mechanics
Sponsored by the MFEM project, the FEM@LLNL Seminar Series focuses on finite element research and applications talks of interest to the MFEM community. On January 20, 2022, Dr. Guglielmo Scovazzi of Duke University presented "The Shifted Boundary Method: An Immersed Approach for Computati
From playlist FEM@LLNL Seminar Series
Ivan Oseledets: QTT FEM solvers for elliptic multiscale problems
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From playlist HIM Lectures: Trimester Program "Multiscale Problems"
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Sponsored by the MFEM project, the FEM@LLNL Seminar Series focuses on finite element research and applications talks of interest to the MFEM community. On March 1, 2022, Raphaël Zanella of the University of Texas at Austin presented "Axisymmetric MFEM-Based Solvers for Compressible Navier
From playlist FEM@LLNL Seminar Series
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Sponsored by the MFEM project, the FEM@LLNL Seminar Series focuses on finite element research and applications talks of interest to the MFEM community. On December 13, 2022, Lin Mu of the University of Georgia presented "An Efficient and Effective FEM Solver for Diffusion Equation with St
From playlist FEM@LLNL Seminar Series