High-Order AFEM for the Laplace–Beltrami Operator: Convergence Rates
| Autor: | J. Manuel Cascón, Ricardo H. Nochetto, Khamron Mekchay, Andrea Bonito, Pedro Morin |
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| Rok vydání: | 2016 |
| Předmět: |
Parametric surfaces
Matemáticas Convergence rates 010103 numerical & computational mathematics 01 natural sciences HIGHER ORDER Mathematics::Numerical Analysis Matemática Pura purl.org/becyt/ford/1 [https] Adaptive Finite Element methods PARAMETRIC SURFACES ADAPTIVE FINITE ELEMENT METHOD Parametric surface FOS: Mathematics Applied mathematics Degree of a polynomial Mathematics - Numerical Analysis 0101 mathematics High order Contraction (operator theory) Higher order Mathematics A posteriori error estimates Applied Mathematics Numerical analysis purl.org/becyt/ford/1.1 [https] Numerical Analysis (math.NA) 010101 applied mathematics Computational Mathematics CONVERGENCE RATES Computational Theory and Mathematics Laplace–Beltrami operator Piecewise LAPLACE–BELTRAMI OPERATOR A POSTERIORI ERROR ESTIMATES CIENCIAS NATURALES Y EXACTAS Analysis |
| Zdroj: | GREDOS. Repositorio Institucional de la Universidad de Salamanca instname CONICET Digital (CONICET) Consejo Nacional de Investigaciones Científicas y Técnicas instacron:CONICET |
| ISSN: | 1615-3383 1615-3375 |
| DOI: | 10.1007/s10208-016-9335-7 |
| Popis: | We present a new AFEM for the Laplace-Beltrami operator with arbitrary polynomial degree on parametric surfaces, which are globally $W^1_\infty$ and piecewise in a suitable Besov class embedded in $C^{1,\alpha}$ with $\alpha \in (0,1]$. The idea is to have the surface sufficiently well resolved in $W^1_\infty$ relative to the current resolution of the PDE in $H^1$. This gives rise to a conditional contraction property of the PDE module. We present a suitable approximation class and discuss its relation to Besov regularity of the surface, solution, and forcing. We prove optimal convergence rates for AFEM which are dictated by the worst decay rate of the surface error in $W^1_\infty$ and PDE error in $H^1$. Comment: 51 pages, the published version contains an additional glossary |
| Databáze: | OpenAIRE |
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