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Bricks for the mixed high-order virtual element method: projectors and differential operators
- Publication Year :
- 2018
-
Abstract
- We present the essential tools to deal with virtual element method (VEM) for the approximation of solutions of partial differential equations in mixed form. Functional spaces, degrees of freedom, projectors and differential operators are described emphasizing how to build them in a virtual element framework and for a general approximation order. To achieve this goal, it was necessary to make a deep analysis on polynomial spaces and decompositions. We exploit such “bricks” to construct virtual element approximations of Stokes, Darcy and Navier–Stokes problems and we provide a series of examples to numerically verify the theoretical behaviour of high-order VEM.
- Subjects :
- Numerical Analysis
Polynomial
Partial differential equation
Series (mathematics)
Applied Mathematics
Numerical analysis
Degrees of freedom (statistics)
Computational mathematics
010103 numerical & computational mathematics
Differential operator
01 natural sciences
Mixed problem
010101 applied mathematics
Algebra
Computational Mathematics
Computational Mathematic
Virtual element method
Mathematics - Numerical Analysis
0101 mathematics
Element (category theory)
Projector
High-order
Numerical Analysi
Polygonal meshe
Mathematics
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....379627452ec3f57364ee9c6d1f7a6b37