An a posteriori error estimator for a non-conforming domain decomposition method for a harmonic elastodynamics equation
We develop a reliable residual-based a posteriori error estimator for a nonconforming method with non-matching meshes for a harmonic elastodynamics equation and show that the approximation method converges with an optimal order to the exact solution. Moreover, we propose an adaptive strategy to redu...
- Autores:
- Tipo de recurso:
- Fecha de publicación:
- 2018
- Institución:
- Universidad Tecnológica de Bolívar
- Repositorio:
- Repositorio Institucional UTB
- Idioma:
- eng
- OAI Identifier:
- oai:repositorio.utb.edu.co:20.500.12585/8883
- Acceso en línea:
- https://hdl.handle.net/20.500.12585/8883
- Palabra clave:
- A posteriori error estimator
Adaptive method
Domain decomposition method
Harmonic elastodinamics equation
Nitsche method
Non-matching mesh
- Rights
- restrictedAccess
- License
- http://creativecommons.org/licenses/by-nc-nd/4.0/
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An a posteriori error estimator for a non-conforming domain decomposition method for a harmonic elastodynamics equation |
| title |
An a posteriori error estimator for a non-conforming domain decomposition method for a harmonic elastodynamics equation |
| spellingShingle |
An a posteriori error estimator for a non-conforming domain decomposition method for a harmonic elastodynamics equation A posteriori error estimator Adaptive method Domain decomposition method Harmonic elastodinamics equation Nitsche method Non-matching mesh |
| title_short |
An a posteriori error estimator for a non-conforming domain decomposition method for a harmonic elastodynamics equation |
| title_full |
An a posteriori error estimator for a non-conforming domain decomposition method for a harmonic elastodynamics equation |
| title_fullStr |
An a posteriori error estimator for a non-conforming domain decomposition method for a harmonic elastodynamics equation |
| title_full_unstemmed |
An a posteriori error estimator for a non-conforming domain decomposition method for a harmonic elastodynamics equation |
| title_sort |
An a posteriori error estimator for a non-conforming domain decomposition method for a harmonic elastodynamics equation |
| dc.subject.keywords.none.fl_str_mv |
A posteriori error estimator Adaptive method Domain decomposition method Harmonic elastodinamics equation Nitsche method Non-matching mesh |
| topic |
A posteriori error estimator Adaptive method Domain decomposition method Harmonic elastodinamics equation Nitsche method Non-matching mesh |
| description |
We develop a reliable residual-based a posteriori error estimator for a nonconforming method with non-matching meshes for a harmonic elastodynamics equation and show that the approximation method converges with an optimal order to the exact solution. Moreover, we propose an adaptive strategy to reduce computational cost and derive better approximations for problems with singularities and with large approximating systems. Numerical experiments confirm theoretical conclusions. © 2018 Global-Science Press. |
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2018 |
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2018 |
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2020-03-26T16:32:33Z |
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2020-03-26T16:32:33Z |
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http://purl.org/coar/version/c_970fb48d4fbd8a85 |
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http://purl.org/coar/resource_type/c_2df8fbb1 |
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info:eu-repo/semantics/article |
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Artículo |
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East Asian Journal on Applied Mathematics; Vol. 8, Núm. 2; pp. 365-384 |
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20797362 |
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https://hdl.handle.net/20.500.12585/8883 |
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10.4208/eajam.100317.020318a |
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Universidad Tecnológica de Bolívar |
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Repositorio UTB |
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45860981700 57212114514 57212113860 |
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East Asian Journal on Applied Mathematics; Vol. 8, Núm. 2; pp. 365-384 20797362 10.4208/eajam.100317.020318a Universidad Tecnológica de Bolívar Repositorio UTB 45860981700 57212114514 57212113860 |
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https://hdl.handle.net/20.500.12585/8883 |
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eng |
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eng |
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Atribución-NoComercial 4.0 Internacional |
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Recurso electrónico |
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application/pdf |
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Global Science Press |
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Global Science Press |
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2020-03-26T16:32:33Z2020-03-26T16:32:33Z2018East Asian Journal on Applied Mathematics; Vol. 8, Núm. 2; pp. 365-38420797362https://hdl.handle.net/20.500.12585/888310.4208/eajam.100317.020318aUniversidad Tecnológica de BolívarRepositorio UTB458609817005721211451457212113860We develop a reliable residual-based a posteriori error estimator for a nonconforming method with non-matching meshes for a harmonic elastodynamics equation and show that the approximation method converges with an optimal order to the exact solution. Moreover, we propose an adaptive strategy to reduce computational cost and derive better approximations for problems with singularities and with large approximating systems. Numerical experiments confirm theoretical conclusions. © 2018 Global-Science Press.Departamento Administrativo de Ciencia, Tecnología e Innovación, COLCIENCIAS: 121565842348, 048-2015 Departamento Administrativo de Ciencia, Tecnología e Innovación, COLCIENCIASThis research work was supported by Colciencias (Departamento Administrativo de Ciencia, Tecnología e Innovación de Colombia) under the project 121565842348 (Contract No. 048-2015). We thank the anonymous reviewers for careful reading of the manuscript and their encouraging comments and suggestions.Recurso electrónicoapplication/pdfengGlobal Science Presshttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/restrictedAccessAtribución-NoComercial 4.0 Internacionalhttp://purl.org/coar/access_right/c_16echttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85075962929&doi=10.4208%2feajam.100317.020318a&partnerID=40&md5=b6f0d94ec48e97dc7b5d668c155b47abAn a posteriori error estimator for a non-conforming domain decomposition method for a harmonic elastodynamics equationinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArtículohttp://purl.org/coar/version/c_970fb48d4fbd8a85http://purl.org/coar/resource_type/c_2df8fbb1A posteriori error estimatorAdaptive methodDomain decomposition methodHarmonic elastodinamics equationNitsche methodNon-matching meshDomínguez C.Torres R.González H.Arnold, D.N., An interior penalty finite element method with discontinuous elements (1982) SIAM J. Numer. Anal., 19, pp. 742-760Becker, R., Mesh adaptation for dirichlet flow control via nitsche’s method (2002) Comm. Numer. Methods Engrg., 18, pp. 669-680Becker, R., Hansbo, P., Stenberg, R., A finite element method for domain decomposition with non-matching grids (2003) Mathematical Modelling and Numerical Analysis, 37, pp. 209-225Boiveau, T., Burman, E., A penalty-free nitsche method for the weak imposition of boundary conditions in compressible and incompressible elasticity (2016) IMA J. Numer. Anal., 36, pp. 770-795Braess, D., Finite elements (2001) Theory, Fast Solvers, and Applications in Solid Mechanics, , Cambridge University PressBrenner, S.C., Scott, L.R., The mathematical theory of finite element methods (2008) Texts in Applied Mathematics, 15. , SpringerCarstensen, C., Dolzmann, G., Funken, S., Helm, D., Locking-free adaptive mixed finite element methods in linear elasticity (2000) Comput. Methods Appl. Mech. Engrg., 190, pp. 1701-1718Domínguez, C., Stephan, E.P., Maischak, M., FE/BE coupling for an acoustic fluid-structure interaction problem. Residual a posteriori error estimates (2012) Internat. J. Numer. Methods Engrg., 89, pp. 299-322Fritz, A., Hüeber, S., Wohlmuth, B., A comparison of mortar and nitsche techniques for linear elasticity (2004) Calcolo, 41, pp. 115-137Hansbo, A., Hansbo, P., Larson, M.G., A finite element method on composite grids based on nitsche’s method (2003) Math. Model. Numer. Anal., 37, pp. 495-514Heinrich, B., Nicaise, S., The nitsche mortar finite-element method for transmission problems with singularities (2003) IMA J. Numer. Anal., 23, pp. 331-358Nitsche, J., Uber ein Variationsprinzip zur Lösung von Dirichlet-Problemen bei Verwendung von Teilräumen, die keinen Randbedingungen unterworfen sind (1971) Abh. Math. Semin. Univ. Hambg., 36, pp. 9-15Verfürth, R., (1996) A Review of A Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques, , Teubner VerlagVerfürth, R., A posteriori error estimation techniques for finite element methods (2013) Numerical Mathematics and Scientific Computation, , Oxford University PressVergara, C., Nitsche’s method for defective boundary value problems in incompressible fluid-dynamics (2011) J. Sci. Comput., 46, pp. 100-123Widlund, O.B., Keyes, D.E., Domain decomposition methods in science and engineering XVI (2007) Lecture Notes in Computational Science and Engineering, 55. , SpringerWohlmuth, B.I., A residual based error estimator for mortar finite element discretizations (1999) Numer. Math., 84, pp. 143-171http://purl.org/coar/resource_type/c_6501THUMBNAILMiniProdInv.pngMiniProdInv.pngimage/png23941https://repositorio.utb.edu.co/bitstream/20.500.12585/8883/1/MiniProdInv.png0cb0f101a8d16897fb46fc914d3d7043MD5120.500.12585/8883oai:repositorio.utb.edu.co:20.500.12585/88832023-04-24 09:55:01.219Repositorio Institucional UTBrepositorioutb@utb.edu.co |