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Journal articles on the topic 'P-finite element method'

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Published: 4 June 2021
Last updated: 19 February 2022

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1

HAN, WEIMIN. "The P-version Penalty Finite Element Method." IMA Journal of Numerical Analysis 12, no. 1 (1992): 47–56. http://dx.doi.org/10.1093/imanum/12.1.47.

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2

Liu, Y., and H. R. Busby. "p-version hybrid/mixed finite element method." Finite Elements in Analysis and Design 30, no. 4 (October 1998): 325–33. http://dx.doi.org/10.1016/s0168-874x(98)00042-0.

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3

Field, David A., and Yoram Pressburger. "Anh-p- multigrid method for finite element analysis." International Journal for Numerical Methods in Engineering 36, no. 6 (March 30, 1993): 893–908. http://dx.doi.org/10.1002/nme.1620360602.

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4

Selvam, R. Panneer, and Zu-Qing Qu. "Adaptive p-finite element method for wind engineering." Wind and Structures 5, no. 2_3_4 (April 25, 2002): 301–16. http://dx.doi.org/10.12989/was.2002.5.2_3_4.301.

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5

Cao, Weiming, and Benqi Guo. "Preconditioning on Element Interfaces for the p-Version Finite Element Method and Spectral Element Method." SIAM Journal on Scientific Computing 21, no. 2 (January 1999): 522–51. http://dx.doi.org/10.1137/s1064827596306951.

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6

Guo, Benqi, and Weiming Cao. "Inexact solvers on element interfaces for the p and h-p finite element method." Computer Methods in Applied Mechanics and Engineering 150, no. 1-4 (December 1997): 173–89. http://dx.doi.org/10.1016/s0045-7825(97)00095-9.

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7

Akin, J. E., and M. Singh. "Object-oriented Fortran 90 P-adaptive finite element method." Advances in Engineering Software 33, no. 7-10 (July 2002): 461–68. http://dx.doi.org/10.1016/s0965-9978(02)00048-0.

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8

Guo, B., and I. Babuška. "The h-p version of the finite element method." Computational Mechanics 1, no. 1 (March 1986): 21–41. http://dx.doi.org/10.1007/bf00298636.

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9

Guo, B., and I. Babuška. "The h-p version of the finite element method." Computational Mechanics 1, no. 3 (September 1986): 203–20. http://dx.doi.org/10.1007/bf00272624.

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10

Guo, Benqi, and Weiming Cao. "Domain decomposition method for the h-p version finite element method." Computer Methods in Applied Mechanics and Engineering 157, no. 3-4 (May 1998): 425–40. http://dx.doi.org/10.1016/s0045-7825(97)00249-1.

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11

Babuška, I., and H. C. Elman. "Performance of theh-p version of the finite element method with various elements." International Journal for Numerical Methods in Engineering 36, no. 15 (August 15, 1993): 2503–23. http://dx.doi.org/10.1002/nme.1620361502.

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12

Pavarino, Luca F. "Schwarz methods with local refinement for the p-version finite element method." Numerische Mathematik 69, no. 2 (December 1994): 185–211. http://dx.doi.org/10.1007/s002110050087.

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13

Zolotareva, N. D., and E. S. Nikolaev. "Stagnation in the p-version of the finite element method." Moscow University Computational Mathematics and Cybernetics 38, no. 3 (July 2014): 91–99. http://dx.doi.org/10.3103/s0278641914030108.

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14

Farhloul, Mohamed, and Hassan Manouzi. "On a mixed finite element method for the p-Laplacian." Rocky Mountain Journal of Mathematics 8, no. 1 (April 2000): 67–78. http://dx.doi.org/10.1216/camq/1008957338.

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15

Korneev, Vadim G., and Søren Jensen. "Preconditioning of the p-version of the finite element method." Computer Methods in Applied Mechanics and Engineering 150, no. 1-4 (December 1997): 215–38. http://dx.doi.org/10.1016/s0045-7825(97)00090-x.

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16

Fish, J., and R. Guttal. "The p-version of finite element method for shell analysis." Computational Mechanics 16, no. 5 (August 1995): 328–40. http://dx.doi.org/10.1007/bf00350722.

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17

Fish, J., and R. Guttal. "The p -version of finite element method for shell analysis." Computational Mechanics 16, no. 5 (August 1, 1995): 328–40. http://dx.doi.org/10.1007/s004660050077.

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18

Liu, D. J., and Z. R. Chen. "The adaptive finite element method for the P-Laplace problem." Applied Numerical Mathematics 152 (June 2020): 323–37. http://dx.doi.org/10.1016/j.apnum.2019.11.018.

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19

Suhuan, Chen, Liang Ping, and Han Wanzhi. "M-P inverse topological variation method of finite element structures." Applied Mathematics and Mechanics 19, no. 3 (March 1998): 289–301. http://dx.doi.org/10.1007/bf02453393.

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20

Zhang, Xiu Ye &. Shangyou. "A Weak Galerkin Finite Element Method for $p$-Laplacian Problem." East Asian Journal on Applied Mathematics 11, no. 2 (June 2021): 219–33. http://dx.doi.org/10.4208/eajam.020920.251220.

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21

Surana, Karan S., Celso H. Carranza, and Sri Sai Charan Mathi. "k-Version of Finite Element Method for BVPs and IVPs." Mathematics 9, no. 12 (June 9, 2021): 1333. http://dx.doi.org/10.3390/math9121333.

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The paper presents k-version of the finite element method for boundary value problems (BVPs) and initial value problems (IVPs) in which global differentiability of approximations is always the result of the union of local approximations. The higher order global differentiability approximations (HGDA/DG) are always p-version hierarchical that permit use of any desired p-level without effecting global differentiability. HGDA/DG are true Ci, Cij, Cijk, hence the dofs at the nonhierarchical nodes of the elements are transformable between natural and physical coordinate spaces using calculus. This is not the case with tensor product higher order continuity elements discussed in this paper, thus confirming that the tensor product approximations are not true Ci, Cijk, Cijk approximations. It is shown that isogeometric analysis for a domain with more than one patch can only yield solutions of class C0. This method has no concept of finite elements and local approximations, just patches. It is shown that compariso of this method with k-version of the finite element method is meaningless. Model problem studies in R2 establish accuracy and superior convergence characteristics of true Cijp-version hierarchical local approximations presented in this paper over tensor product approximations. Convergence characteristics of p-convergence, k-convergence and pk-convergence are illustrated for self adjoint, non-self adjoint and non-linear differential operators in BVPs. It is demonstrated that h, p and k are three independent parameters in all finite element computations. Tensor product local approximations and other published works on k-version and their limitations are discussed in the paper and are compared with present work.
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22

Gui, W., and I. Babuška. "Theh,p andh-p versions of the finite element method in 1 dimension." Numerische Mathematik 49, no. 6 (November 1986): 577–612. http://dx.doi.org/10.1007/bf01389733.

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23

Gui, W., and I. Babuška. "Theh, p andh-p versions of the finite element method in 1 dimension." Numerische Mathematik 49, no. 6 (November 1986): 613–57. http://dx.doi.org/10.1007/bf01389734.

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24

Gui, W., and I. Babuška. "Theh, p andh-p versions of the finite element method in 1 dimension." Numerische Mathematik 49, no. 6 (November 1986): 659–83. http://dx.doi.org/10.1007/bf01389735.

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25

Babuška, Ivo, and Manil Suri. "The p- and h-p versions of the finite element method, an overview." Computer Methods in Applied Mechanics and Engineering 80, no. 1-3 (June 1990): 5–26. http://dx.doi.org/10.1016/0045-7825(90)90011-a.

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26

Nguyen, Tam H., Chau H. Le, and Jerome F. Hajjar. "Topology optimization using the p-version of the finite element method." Structural and Multidisciplinary Optimization 56, no. 3 (March 16, 2017): 571–86. http://dx.doi.org/10.1007/s00158-017-1675-7.

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27

Thompson, Lony L., and Peter M. Pinsky. "Complex wavenumber Fourier analysis of the p-version finite element method." Computational Mechanics 13, no. 4 (July 1994): 255–75. http://dx.doi.org/10.1007/bf00350228.

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28

Tin-Loi, F., and N. S. Ngo. "Performance of the p-version finite element method for limit analysis." International Journal of Mechanical Sciences 45, no. 6-7 (June 2003): 1149–66. http://dx.doi.org/10.1016/j.ijmecsci.2003.08.004.

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29

Tin-Loi, F., and N. S. Ngo. "Performance of a p-adaptive finite element method for shakedown analysis." International Journal of Mechanical Sciences 49, no. 10 (October 2007): 1166–78. http://dx.doi.org/10.1016/j.ijmecsci.2007.02.004.

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30

A. Szabó, Barna. "Mesh design for the p-version of the finite element method." Computer Methods in Applied Mechanics and Engineering 55, no. 1-2 (April 1986): 181–97. http://dx.doi.org/10.1016/0045-7825(86)90091-5.

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31

Mandel, Jan. "Iterative solvers by substructuring for the p-version finite element method." Computer Methods in Applied Mechanics and Engineering 80, no. 1-3 (June 1990): 117–28. http://dx.doi.org/10.1016/0045-7825(90)90017-g.

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32

Kuo, Yong-Lin, William L. Cleghorn, and Kamran Behdinan. "HAMILTONIAN AS ERROR INDICATOR IN THE P-VERSION OF FINITE ELEMENT METHOD." Transactions of the Canadian Society for Mechanical Engineering 34, no. 2 (June 2010): 215–23. http://dx.doi.org/10.1139/tcsme-2010-0013.

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This paper presents the Hamiltonian-based error analysis applied to two-dimensional elasostatic problems. The accuracy enhancement is achieved by using the p-version of finite element method. The results show that the Hamiltonian error has faster rates of convergence at lower order of interpolation polynomials to compare with the energy error, and the Hamiltonian error clearly indicates great error reductions at a certain polynomial order. This can not only obtain an accurate enough solution but also save extra computational time. Another strategy is presented by computing the residual of the Hamiltonian-based governing equations. Relative values of residuals between elements can provide an index of selecting the best polynomial orders. Illustrative examples show the validities of the two approaches.
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33

BABUŠKA, IVO, UDAY BANERJEE, and JOHN E. OSBORN. "GENERALIZED FINITE ELEMENT METHODS — MAIN IDEAS, RESULTS AND PERSPECTIVE." International Journal of Computational Methods 01, no. 01 (June 2004): 67–103. http://dx.doi.org/10.1142/s0219876204000083.

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This paper is an overview of the main ideas of the Generalized Finite Element Method (GFEM). We present the basic results, experiences with, and potentials of this method. GFEM is a generalization of the classical Finite Element Method — in its h, p, and h-p versions — as well as of the various forms of meshless methods used in engineering.
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34

Huang, Yong, De Jun Ma, W. Chen, Jia Liang Wang, and Liang Sun. "Finite Element Simulation and Experimental Analysis of O-P Hardness." Advanced Materials Research 1033-1034 (October 2014): 462–65. http://dx.doi.org/10.4028/www.scientific.net/amr.1033-1034.462.

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Based on the finite element analysis method to simulate the O-P hardness. Taking S45C steel as an example, comparative analysis of O-P hardness of finite element simulation and O-P hardness of instrument indentation hardness experiment, results show that difference of S45C steel’s O-P hardness between the finite element simulation and real experiment is-2.62% Accordingly seen, O-P hardness can be obtained by finite element numerical simulation method, it’s a possible way to study relations between O-P hardness and Vickers hardness based on finite element numerical simulation techniques.
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35

Shi, Yu, Hong Ling Meng, Qian Jia, and Dong Yang Shi. "Superconvergence Analysis of Finite Element Method for Onlinear Klein-Gordon Equation." Applied Mechanics and Materials 527 (February 2014): 343–46. http://dx.doi.org/10.4028/www.scientific.net/amm.527.343.

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The standard finite elements of degree p over the rectangular meshes are applied to a non-linear Klein-Gordon equation. By utilizing the properties of interpolation on the element, high accuracy analysis and derivative delivery techniques with respect to time t instead of the traditional Ritz projection operator, which is an indispensable tool in the traditional finite element analysis, the supercloseproperty with order is obtained. Furthermore, the superconvergence result is derived through the postprocessing approach.
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36

Szabó, Barna A. "The p- and h-p versions of the finite element method in solid mechanics." Computer Methods in Applied Mechanics and Engineering 80, no. 1-3 (June 1990): 185–95. http://dx.doi.org/10.1016/0045-7825(90)90022-e.

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37

Wang, Jie Fang, and Wei Guang An. "P-SS Algorithm for Solving the Eigenvalue Problem of Finite Element System." Applied Mechanics and Materials 300-301 (February 2013): 1118–21. http://dx.doi.org/10.4028/www.scientific.net/amm.300-301.1118.

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P-SS algorithm for solving eigenvalue problem was obtained, based on the power method and the similar shrinkage method. This algorithm can be used to not only solve all eigenvalues of small system, but also partial eigenvalues of large finite element system. The calculation program of this algorithm is universal and practical. Compared with the existing methods, the error of P-SS method is very small, and it signify that the new method is feasible and convenient.
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38

Strug, Barbara, Anna Paszynśka, Maciej Paszynśki, and Ewa Grabska. "Using a graph grammar system in the finite element method." International Journal of Applied Mathematics and Computer Science 23, no. 4 (December 1, 2013): 839–53. http://dx.doi.org/10.2478/amcs-2013-0063.

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Abstract The paper presents a system of Composite Graph Grammars (CGGs)modelling adaptive two dimensional hp Finite Element Method (hp-FEM) algorithms with rectangular finite elements. A computational mesh is represented by a composite graph. The operations performed over the mesh are defined by the graph grammar rules. The CGG system contains different graph grammars defining different kinds of rules of mesh transformations. These grammars allow one to generate the initial mesh, assign values to element nodes and perform h- and p-adaptations. The CGG system is illustrated with an example from the domain of geophysics.
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39

Ilyas, Muhammad, and Bishnu P. Lamichhane. "Optimal parameter for the stabilised five-field extended Hu–Washizu formulation." ANZIAM Journal 61 (August 11, 2020): C197—C213. http://dx.doi.org/10.21914/anziamj.v61i0.15176.

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We present a mixed finite element method for the elasticity problem. We expand the standard Hu–Washizu formulation to include a pressure unknown and its Lagrange multiplier. By doing so, we derive a five-field formulation. We apply a biorthogonal system that leads to an efficient numerical formulation. We address the coercivity problem by adding a stabilisation term with a parameter. We also present an analysis of the optimal choices of parameter approximation. References I. Babuska and T. Strouboulis. The finite element method and its reliability. Oxford University Press, New York, 2001. https://global.oup.com/academic/product/the-finite-element-method-and-its-reliability-9780198502760?cc=au&lang=en&. D. Braess. Finite Elements: Theory, Fast Solvers, and Applications in Solid Mechanics. Cambridge University Press, Cambridge, UK, 3rd edition edition, 2007. doi:10.1017/CBO9780511618635. J. K. Djoko and B. D. Reddy. An extended Hu–Washizu formulation for elasticity. Comput. Meth. Appl. Mech.Eng. 195(44):6330–6346, 2006. doi:10.1016/j.cma.2005.12.013. J. Droniou, M. Ilyas, B. P. Lamichhane, and G. E. Wheeler. A mixed finite element method for a sixth-order elliptic problem. IMA J. Numer. Anal. 39(1):374–397, 2017. doi:10.1093/imanum/drx066. M. Ilyas. Finite element methods and multi-field applications. PhD thesis, University of Newcastle, 2019. http://hdl.handle.net/1959.13/1403421. M. Ilyas and B. P. Lamichhane. A stabilised mixed finite element method for the Poisson problem based on a three-field formulation. In Proceedings of the 12th Biennial Engineering Mathematics and Applications Conference, EMAC-2015, volume 57 of ANZIAM J. pages C177–C192, 2016. doi:10.21914/anziamj.v57i0.10356. M. Ilyas and B. P. Lamichhane. A three-field formulation of the Poisson problem with Nitsche approach. In Proceedings of the 13th Biennial Engineering Mathematics and Applications Conference, EMAC-2017, volume 59 of ANZIAM J. pages C128–C142, 2018. doi:10.21914/anziamj.v59i0.12645. B. P. Lamichhane. Two simple finite element methods for Reissner–Mindlin plates with clamped boundary condition. Appl. Numer. Math. 72:91–98, 2013. doi:10.1016/j.apnum.2013.04.005. B. P. Lamichhane and E. P. Stephan. A symmetric mixed finite element method for nearly incompressible elasticity based on biorthogonal systems. Numer. Meth. Part. Diff. Eq. 28(4):1336–1353, 2011. doi:10.1002/num.20683. B. P. Lamichhane, A. T. McBride, and B. D. Reddy. A finite element method for a three-field formulation of linear elasticity based on biorthogonal systems. Comput. Meth. Appl. Mech. Eng. 258:109–117, 2013. doi:10.1016/j.cma.2013.02.008. J. C. Simo and F. Armero. Geometrically non-linear enhanced strain mixed methods and the method of incompatible modes. Int. J. Numer. Meth. Eng. 33(7):1413–1449, may 1992. doi:10.1002/nme.1620330705. A. Zdunek, W. Rachowicz, and T. Eriksson. A five-field finite element formulation for nearly inextensible and nearly incompressible finite hyperelasticity. Comput. Math. Appl. 72(1):25–47, 2016. doi:10.1016/j.camwa.2016.04.022.
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40

Zhang, Jian Ming, and Yong He. "New Development of the P and H-P Version Finite Element Method with Quasi-Uniform Meshes for Elliptic Problems." Applied Mechanics and Materials 444-445 (October 2013): 671–75. http://dx.doi.org/10.4028/www.scientific.net/amm.444-445.671.

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In recent three decades, the finite element method (FEM) has rapidly developed as an important numerical method and used widely to solve large-scale scientific and engineering problems. In the fields of structural mechanics such as civil engineering , automobile industry and aerospace industry, the finite element method has successfully solved many engineering practical problems, and it has penetrated almost every field of today's sciences and engineering, such as material science, electricmagnetic fields, fluid dynamics, biology, etc. In this paper, we will overview and summarize the development of the p and h-p version finite element method, and introduce some recent new development and our newest research results of the p and h-p version finite element method with quasi-uniform meshes in three dimensions for elliptic problems.
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41

Suri, Manil. "The p and hp finite element method for problems on thin domains." Journal of Computational and Applied Mathematics 128, no. 1-2 (March 2001): 235–60. http://dx.doi.org/10.1016/s0377-0427(00)00514-8.

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42

Belenki, L., L. Diening, and C. Kreuzer. "Optimality of an adaptive finite element method for the p-Laplacian equation." IMA Journal of Numerical Analysis 32, no. 2 (July 16, 2011): 484–510. http://dx.doi.org/10.1093/imanum/drr016.

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43

Királyfalvi, György, and Barna A. Szabó. "Quasi-regional mapping for the p-version of the finite element method." Finite Elements in Analysis and Design 27, no. 1 (September 1997): 85–97. http://dx.doi.org/10.1016/s0168-874x(97)00006-1.

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44

Babuška, I., and Manil Suri. "The $h-p$ version of the finite element method with quasiuniform meshes." ESAIM: Mathematical Modelling and Numerical Analysis 21, no. 2 (1987): 199–238. http://dx.doi.org/10.1051/m2an/1987210201991.

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45

Eriksson, Kenneth. "Some Error Estimates for the p-Version of the Finite Element Method." SIAM Journal on Numerical Analysis 23, no. 2 (April 1986): 403–11. http://dx.doi.org/10.1137/0723027.

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46

Wang, Y., P. Monk, and B. Szabo. "Computing cavity modes using the p-version of the finite element method." IEEE Transactions on Magnetics 32, no. 3 (May 1996): 1934–40. http://dx.doi.org/10.1109/20.492889.

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47

Babuška, I., and Manil Suri. "The $p$-version of the finite element method for constraint boundary conditions." Mathematics of Computation 51, no. 183 (September 1, 1988): 1. http://dx.doi.org/10.1090/s0025-5718-1988-0942140-7.

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48

Babuska, I., and Manil Suri. "The p-Version of the Finite Element Method for Constraint Boundary Conditions." Mathematics of Computation 51, no. 183 (July 1988): 1. http://dx.doi.org/10.2307/2008576.

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49

Guo, Benqi, and Hae-Soo Oh. "Theh-p version of the finite element method for problems with interfaces." International Journal for Numerical Methods in Engineering 37, no. 10 (May 30, 1994): 1741–62. http://dx.doi.org/10.1002/nme.1620371007.

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50

Babuška, I., and Hae-Soo Oh. "Pollution problem of thep- andh-p versions of the finite element method." Communications in Applied Numerical Methods 3, no. 6 (November 1987): 553–61. http://dx.doi.org/10.1002/cnm.1630030617.

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