A numerical comparison of high order transformation and isoparametric transformation methods

DOI10.1016/0898-1221(79)90085-3zbMath0441.65010OpenAlexW1993418640MaRDI QIDQ1143121

S. H. Smith

Publication date: 1979

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0898-1221(79)90085-3

zbMATH Keywords

finite element methodLaplace's equationnumerical comparisonasymptotic error estimatescurved domainshigh order transformation methodquadratic isoparametric transformation method

Mathematics Subject Classification ID

Finite element methods applied to problems in solid mechanics (74S05) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Numerical interpolation (65D05) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Multidimensional problems (41A63) Interpolation in approximation theory (41A05)

Related Items (5)

On the stability of two-dimensional interpolation and high order bases for curved finite elements ⋮ Integration techniques for isoparametric and higher order bases on finite elements with a curved side ⋮ Rational basis functions for curved elements ⋮ Generalized Gaussian quadrature rules over regions with parabolic edges ⋮ Recursive calculation of curved finite element stiffness matrices

Cites Work

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• Evaluation of integrals for a ten-node isoparametric tetrahedral finite element
• L\(^2\) error estimates for finite elements with interpolated boundary conditions
• High Order Transformation Methods for Curved Finite Elements
• A new family of curvilinear plate bending elements for vibration and stability
• Finite element analysis of plates with curved edges

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