Stability, accuracy, and efficiency of some underintegrated methods in finite element computations

DOI10.1016/0045-7825(85)90097-0zbMath0579.65110OpenAlexW2087612294MaRDI QIDQ1067385

B. George

Publication date: 1985

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0045-7825(85)90097-0

zbMATH Keywords

Laplace equationstiffness matricesnumerical instabilitiesspurious modesnumerical quadrature formulaUnderintegration

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32)

Related Items (2)

New improved hourglass control for bilinear and trilinear elements in anisotropic linear elasticity ⋮ An accurate and efficient a posteriori control of hourglass instabilities in underintegrated linear and nonlinear elasticity

Cites Work

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• Analysis of hourglass instabilities and control in underintegrated finite element methods
• A stabilization matrix for the bilinear Mindlin plate element
• A uniform strain hexahedron and quadrilateral with orthogonal hourglass control
• A stabilization procedure for the quadrilateral plate element with one‐point quadrature
• Theory of a Finite Difference Method on Irregular Networks
• Optimal L ∞ Estimates for the Finite Element Method on Irregular Meshes
• Nonelliptic Approximation of a Class of Partial Differential Equations with Neumann Boundary Condition

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