Publicación: A PRIORI AND A POSTERIORI ERROR ESTIMATES FOR A VIRTUAL ELEMENT SPECTRAL ANALYSIS FOR THE ELASTICITY EQUATIONS
| dc.creator | DAVID ANDRÉS MORA HERRERA | |
| dc.date | 2020 | |
| dc.date.accessioned | 2025-01-10T15:13:14Z | |
| dc.date.available | 2025-01-10T15:13:14Z | |
| dc.date.issued | 2020 | |
| dc.description.abstract | WE PRESENT A PRIORI AND A POSTERIORI ERROR ANALYSIS OF A VIRTUAL ELEMENT METHOD (VEM) TO APPROXIMATE THE VIBRATION FREQUENCIES AND MODES OF AN ELASTIC SOLID. WE ANALYZE A VARIATIONAL FORMULATION RELYING ONLY ON THE SOLID DISPLACEMENT AND PROPOSE AN $H^1({\OMEGA})$-CONFORMING DISCRETIZATION BY MEANS OF VEM. UNDER STANDARD ASSUMPTIONS ON THE COMPUTATIONAL DOMAIN, WE SHOW THAT THE RESULTING SCHEME PROVIDES A CORRECT APPROXIMATION OF THE SPECTRUM AND PROVE AN OPTIMAL ORDER ERROR ESTIMATE FOR THE EIGENFUNCTIONS AND A DOUBLE ORDER FOR THE EIGENVALUES. SINCE, THE VEM HAS THE ADVANTAGE OF USING GENERAL POLYGONAL MESHES, WHICH ALLOWS IMPLEMENTING EFFICIENTLY MESH REFINEMENT STRATEGIES, WE ALSO INTRODUCE A RESIDUAL-TYPE A POSTERIORI ERROR ESTIMATOR AND PROVE ITS RELIABILITY AND EFFICIENCY. WE USE THE CORRESPONDING ERROR ESTIMATOR TO DRIVE AN ADAPTIVE SCHEME. FINALLY, WE REPORT THE RESULTS OF A COUPLE OF NUMERICAL TESTS THAT ALLOW US TO ASSESS THE PERFORMANCE OF THIS APPROACH. | |
| dc.format | application/pdf | |
| dc.identifier.doi | 10.1093/imanum/dry063 | |
| dc.identifier.issn | 1464-3642 | |
| dc.identifier.issn | 0272-4979 | |
| dc.identifier.uri | https://repositorio.ubiobio.cl/handle/123456789/10984 | |
| dc.language | spa | |
| dc.publisher | IMA JOURNAL OF NUMERICAL ANALYSIS | |
| dc.relation.uri | 10.1093/imanum/dry063 | |
| dc.rights | PUBLICADA | |
| dc.title | A PRIORI AND A POSTERIORI ERROR ESTIMATES FOR A VIRTUAL ELEMENT SPECTRAL ANALYSIS FOR THE ELASTICITY EQUATIONS | |
| dc.title.alternative | ESTIMACIONES DE ERRORES A PRIORI Y A POSTERIORI PARA UN ANÁLISIS ESPECTRAL DE ELEMENTOS VIRTUALES PARA LAS ECUACIONES DE ELASTICIDAD | |
| dc.type | ARTÍCULO | |
| dspace.entity.type | Publication | |
| ubb.Estado | PUBLICADA | |
| ubb.Otra Reparticion | DEPARTAMENTO DE MATEMATICA | |
| ubb.Sede | CONCEPCIÓN |
