×

zbMATH — the first resource for mathematics

Mesh design for the p-version of the finite element method. (English) Zbl 0587.73106
When properly designed meshes are used then the performance of the p- extension is very close to the best performance attainable by the finite element method. Proper mesh design depends on the exact solution, however. Because the exact solution is not known a priori, initial mesh design is generally based on certain assumptions concerning the exact solution which must be tested in the post-solution phase to ensure reliability and accuracy of data computed from the finite element solution. In this paper general guidelines are presented for prior design of meshes, and procedures for post-solution testing are described and illustrated by examples.

MSC:
74S05 Finite element methods applied to problems in solid mechanics
74S99 Numerical and other methods in solid mechanics
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Babuška, I.; Szabó, B.; Katz, I.N., The p-version of the finite element method, SIAM J. numer. anal., 18, 515-545, (1981) · Zbl 0487.65059
[2] Babuška, I.; Szabó, B., On the rates of convergence of the finite element method, Internat. J. numer. meths. engrg., 18, 323-341, (1982) · Zbl 0498.65050
[3] Babuška, I.; Miller, A., The post-processing approach in the finite element method—part 1: calculation of displacements, stresses and other higher derivatives of the displacements, Internat. J. numer. meths. engrg., 20, 1085-1109, (1984) · Zbl 0535.73052
[4] Babuška, I.; Miller, A., The post-processing approach in the finite element method—part 2: the calculation of stress intensity factors, Internat. J. numer. meths. engrg., 20, 1111-1129, (1984) · Zbl 0535.73053
[5] Babuška, I.; Miller, A., The post-processing approach in the finite element method—part 3: A-posteriori error estimates and adaptive mesh selection, Internat. J. numer. meths. engrg., 20, 2311-2324, (1984) · Zbl 0571.73074
[6] Babuška, I.; Gui, W.; Szabó, B.A., Performance of the h, p and h-p versions of the finite element method, () · Zbl 0614.65089
[7] Gui, W., The h-p version of the finite element method for one dimensional problem, ()
[8] Guo, B., The h-p version of the finite element method in two dimensions—mathematical theory and computational experience, ()
[9] Izadpanah, K., Computation of the stress components in the p-version of the finite element method, ()
[10] Nuismer, R.J.; Whitney, J.M., Uniaxial failure of composite laminates containing stress concentrations, (), 117
[11] Nuismer, R.J.; Labor, J.D., Applications of average stress failure criterion: part I—tension, J. composite materials, 12, 238, (1978)
[12] Potter, R.T., On the mechanism of tensile fracture in notched fibre reinforced plastics, (), 325-341
[13] Szabó, B.A.; Babuška, I., Stress approximations by the h- and p-versions of the finite element method, ()
[14] Szabó, B., Estimation and control of error based on p-convergence, (), 61-78
[15] Szabó, B.A., ()
[16] Szabó, B.A., Implementation of a finite element software system with h- and p-extension capabilities, ()
[17] Szabó, B.A., Computation of stress field parameters in areas of steep stress gradients, (), Comm. appl. numer. meths., 1, (1985), also
[18] Vasilopoulos, D., Treatment of geometric singularities with the p-version of the finite element method, () · Zbl 0649.73011
[19] Whitney, J.M.; Nuismer, R.J., Stress fracture criteria for laminated composites containing stress concentrations, J. composite materials, 253-265, (1974)
[20] Williams, M.L., Stress singularities resulting from various boundary conditions in angular corners of plates in extension, J. appl. mech. ASME, 526-528, (1952)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.