Low cost a posteriori error estimators for an augmented mixed FEM in linear elasticity |
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| Institution: | 1. Departamento de Matemática y Física Aplicadas, Universidad Católica de la Santísima Concepción, Concepción, Chile;2. Departamento de Ingeniería Civil, Universidad Católica de la Santísima Concepción, Concepción, Chile;3. Departamento de Matemáticas, Universidade da Coruña, Campus de Elviña s/n, 15071, A Coruña, Spain;4. Basque Center for Applied Mathematics, C/Alameda de Mazarredo 14, 48009, Bilbao, Spain;1. IRMAR & INSA Rennes, France;2. Dpto. de Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Spain;1. Universitá di Firenze, Italy;2. National Cheng Kung University, Taiwan;3. National Taiwan University, Taiwan;1. Fujian Provincial Key Laboratory on Mathematical Modeling and Scientific Computing and School of Mathematical Sciences, Xiamen University, 361005 Xiamen, China;2. Department of Mathematics, Purdue University, West Lafayette, IN 47907, USA;3. Beijing Computational Science Research Center, 100084, Beijing, China;1. Politecnico di Milano, Italy;2. Università di Firenze, Italy;3. National Cheng Kung University, Taiwan;4. National Taiwan University, Taiwan |
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| Abstract: | We consider an augmented mixed finite element method applied to the linear elasticity problem and derive a posteriori error estimators that are simpler and easier to implement than the ones available in the literature. In the case of homogeneous Dirichlet boundary conditions, the new a posteriori error estimator is reliable and locally efficient, whereas for non-homogeneous Dirichlet boundary conditions, we derive an a posteriori error estimator that is reliable and satisfies a quasi-efficiency bound. Numerical experiments illustrate the performance of the corresponding adaptive algorithms and support the theoretical results. |
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| Keywords: | Linear elasticity Mixed finite element method Stabilization A posteriori error estimates |
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