Simplicial finite elements in higher dimensions.

DOI10.1007/s10492-007-0013-6zbMath1164.65493OpenAlexW1970571778MaRDI QIDQ954618

Sergey Korotov, Michal Křížek, Jan H. Brandts

Publication date: 24 November 2008

Published in: Applications of Mathematics (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/33287

zbMATH Keywords

finite element methodsuperconvergencediscrete maximum principlesurvey paper\(n\)-simplexstrengthened Cauchy-Schwarz inequality

Mathematics Subject Classification ID

Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)

Related Items (8)

Construction and shape optimization of simplicial meshes in \(d\)-dimensional space ⋮ Properties of the multidimensional finite elements ⋮ Enabling four-dimensional conformal hybrid meshing with cubic pyramids ⋮ The discrete maximum principle for Galerkin solutions of elliptic problems ⋮ Red refinements of simplices into congruent subsimplices ⋮ Discrete maximum principle for finite element parabolic models in higher dimensions ⋮ Discrete advection-diffusion equations on graphs: maximum principle and finite volumes ⋮ Stable subdivision of 4D polytopes

Uses Software

• FEMLAB
• COMSOL

Cites Work

• On superconvergence techniques
• Two simple derivations of universal bounds for the CBS inequality constant.
• Dissection of the path-simplex in \(\mathbb {R}^n\) into \(n\) path-subsimplices
• Trisecting an orthoscheme
• Mixed finite elements in \(\mathbb{R}^3\)
• Upper bound of the constant in strengthened C.B.S. inequality for systems of linear partial differential equations
• Discrete maximum principles for finite element solutions of nonlinear elliptic problems with mixed boundary conditions
• Finite element exterior calculus, homological techniques, and applications
• Pointwise superconvergence of the gradient for the linear tetrahedral element
• Gradient superconvergence on uniform simplicial partitions of polytopes
• Strengthened Cauchy-Bunyakowski-Schwarz inequality for a three-dimensional elasticity system
• Nested tetrahedral grids and strengthened C.B.S. inequality
• Uniform estimate of the constant in the strengthened CBS inequality for anisotropic non‐conforming FEM systems
• Exact solution of certain problems by finite- element method.
• An Optimal Adaptive Finite Element Method
• Numerical Analysis and Its Applications
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