The h, p and h-p version of the finite element method; basis theory and applications
References (61)
- et al.
Basic principles of feedback and adaptive approaches in the finite element method
Comput. Methods Appl. Mech. Engrg.
(1986) - et al.
The h-p version of the finite element method for problems with nonhomogeneous essential boundary conditions
Comput. Methods Appl. Mech. Engrg.
(1989) - et al.
Quality assessment of the a-posteriori error estimation in finite elements
Finite Elements in Analysis and Design
(1992) - et al.
The h-p version of the finite element method with quasi-uniform meshes, RAIRO
Math. Modelling and Numer. Anal.
(1987) Elliptic Problems in Nonsmooth Domains
(1985)- et al.
Toward a universal h-p adaptive element strategy, III. Design of h-p meshes
Comput. Methods Appl. Mech. Engrg.
(1989) - et al.
The three R's of engineering analysis and error estimation and adaptivity
Comput. Methods. Appl. Mech. Engrg.
(1990) - et al.
Superconvergence recovery technique and a posteriori error estimators
Internat. J. Numer. Methods Engrg.
(1990) - et al.
A unified approach to a posteriori error estimation based on element residual methods
(1991)
Reliable stress and fracture mechanics analysis of complex aircraft component using an h-p version of FEM
Computation of the vertex singularity factors for laplace equation in 3 dimensions
Error estimate for the combined h and p versions of the finite element method
Numer. Math.
(1981)
Analysis of the efficiency of an a-posteriori error estimator for linear triangular finite elements
SIAM J. Numer. Anal.
(1992)
Regularity of the solutions of elliptic problem with piecewise analytic data, Part I: boundary value problems for linear elliptic equation of second order
SIAM J. Math. Anal.
(1988)
The h-p version of the finite element method for domains with curved boundaries
SIAM J. Numer. Anal.
(1988)
The theory and practice of the h-p version of the finite element method
Regularity of the solutions of elliptic problem with piecewise analytic data, Part II. The trace spaces and application to the boundary value problems with nonhomogeneous boundary conditions
SIAM J. Math. Anal.
(1989)
Regularity and numerical solution of eigenvalue problems with piecewise analytic data
SIAM J. Numer. Anal.
(1989)
Implementation of nonhomogeneous Dirichlet boundary conditions in the p-version of the finite element method
Impact Comp. Sci. Engrg.
(1989)
An expert system for optimal mesh design in the h-p version of the finite element method
Internat. J. Numer. Methods Engrg.
(1987)
A posteriori error estimates for adaptive finite element computations
SIAM J. Numer. Anal.
(1978)
Analysis of optimal finite element meshes in R1
Math. Comp.
(1979)
A posteriori error estimators in the finite element method
Internat. J. Numer. Methods Engrg.
(1978)
et al.A posteriori error estimators in the finite element method
Internat. J. Numer. Methods Engrg.
(1978)
Reliable error estimation and mesh adaptation for the finite element method
The p- and h-p version of the finite element method. An Overview
Comput. Methods Appl. Mech. Engrg.
(1990)
The p-version of the finite element methods
SIAM J. Numer. Anal.
(1981)
Feedback and adaptive finite element solution of one-dimensional boundary value problems
Numer. Math.
(1984)
Asymptotically exact a posteriori error estimator for biquadratic elements
Finite Elements in Analysis and Design
(1987)
Some a-posteriori error estimators for elliptic partial differential equations
Math. Comp.
(1985)
Cited by (121)
Adaptive Isogeometric Analysis using optimal transport and their fast solvers
2024, Computer Methods in Applied Mechanics and EngineeringShape optimization for the strong routing of light in periodic diffraction gratings
2023, Journal of Computational PhysicsCitation Excerpt :Equations (29) and (30) are used in order to measure the quality of our numerical solution strategy that is introduced in the following section. To use the exact parameterization of shapes, we employ curvilinear elements [57] and bend the edges of an initial mesh of good quality. Curved boundaries or interfaces are implemented by a bilinear transfinite interpolant [58,59], where the parameterization of curved edges are available.
Fully automatic multigrid adaptive mesh refinement strategy with controlled accuracy for nonlinear quasi-static problems
2022, Computer Methods in Applied Mechanics and EngineeringA spline-based FE approach to modelling of high frequency dynamics of 1-D structures
2021, Computers and Mathematics with ApplicationsFast evaluation of finite element weak forms using python tensor contraction packages
2021, Advances in Engineering Software
- ∗
Partially supported by the Office of Naval Research under Grant N00014-90-J1030.
- ‡
Partially supported by the National Science and Engineering Research Council of Canada, under Grant OGP00 46726.
Copyright © 1992 Published by Elsevier Ltd.