Applications of Mathematics · 1982 · 38 citations · 3 references
EngineeringComputational EngineeringMechanical EngineeringComputational MechanicsFinite Element AnalysisFinite Element MethodsConvergence AnalysisElasticity TheoryFinite Element DiscretizationFinite Element FormulationSolid Mechanics ApplicationsStructural Finite Element AnalysisElasticity ProblemsFinite Element Methods In ElasticityFinite Element ModelingStiffness Matrix Formulation
The tetrahedral stress element is introduced and two different types of a finite piecewise linear approximation of the dual elasticity problem are investigated on a polyhedral domain. Fot both types a priori error estimates $O(h^2)$ in $L_2$-norm and $O(h^{1/2})$ in $L_\infty$-norm are established, provided the solution is smooth enough. These estimates are based on the fact that for any polyhedron there exists a strongly regular family of decomprositions into tetrahedra, which is proved in the paper, too.
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