1 |
I. Babuska, R.B. Kellogg, and J. Pitkaranta, Direct and inverse error estimates for finite elements with mesh refinements, Numer. Math., 33 (1979), 447-471.
DOI
|
2 |
H. Blum and M. Dobrowolski, On finite element methods for elliptic equations on domains with corners, Computing, 28 (1982), 53-63.
DOI
|
3 |
M. Bourlard, M. Dauge, M.-S. Lubuma, and S. Nicaise, Coefficients of the singularities for elliptic boundary value problems on domains with conical points III. Finite element methods on polygonal domains, SIAM Numer. Anal., 29 (1992), 136-155.
DOI
|
4 |
S. C. Brenner, Multigrid methods for the computation of singular solutions and stress intensity factor I: Corner singularities, Math. Comp., 68 (226), (1999), 559-583.
DOI
|
5 |
S. C. Brenner and L.-Y. Sung, Multigrid methods for the computation of singular solutions and stress intensity factors III: Interface singularities, Comput. Methods Appl. Mech. Engrg. 192(2003), 4687-4702.
DOI
|
6 |
Z. Chen and S. Dai, On the efficiency of adaptive finite element methods for elliptic problems with discontinuous coefficients, SIAM J. Sci. Comput., 24:(2002), 443-462.
DOI
|
7 |
Z. Cai and S.C. Kim, A finite element method using singular functions for the poisson equation: Corner singularities, SIAM J. Numer. Anal., 39:(2001), 286-299.
DOI
|
8 |
Z. Cai , S.C. Kim, S.D. Kim, S. Kong, A finite element method using singular functions for Poisson equations: Mixed boundary conditions, Comput. Methods Appl. Mech. Engrg. 195 (2006) 26352648
DOI
|
9 |
M. Djaoua, Equations Integrales pour un Probleme Singulier dans le Plan, These de Troisieme Cycle, Universite Pierre et Marie Curie, Paris, 1977.
|
10 |
M. Dobrowolski, Numerical Approximation of Elliptic Interface and Corner Problems, Habilitationsschrift, Bonn, 1981.
|
11 |
G. J. Fix, S. Gulati, and G. I. Wakoff, On the use of singular functions with finite elements approximations, J. Comput. Phy., 13 (1973), 209-228.
DOI
|
12 |
D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, 2nd ed., Springer-Verlag, Berlin, 1983.
|
13 |
P. Grisvard, Elliptic Problems in Nonsmooth Domains, Pitman, Boston, MA, 1985.
|
14 |
F. Hecht, New development in FreeFem++, J. Numer. Math. 20 (2012), no. 3-4, 251265.
|
15 |
S. Kim and H.C. Lee, A finite element method for computing accurate solutions for Poisson equations with corner singularities using the stress intensity factor, Computers and Mathematics with Applications, 71(2016) 2330-2337.
DOI
|
16 |
V. Mazya and B. Plamenevskii, On the coefficients in the asymptotics of solutions of elliptic boundary-value problems near conical points, Soviet Math. Dokl., 15 (1974), 1570-1575.
|
17 |
V. G. Mazya and B. A. Plamenevskii, Coefficients in the asymptotics of the solutions of an elliptic boundary value problem in a cone, J. Soviet Math., 9 (1978), 750-764.
DOI
|
18 |
P. Morin, R.H. Nochetto, and K.G. Siebert Data oscillation and convergence of adaptive FEM, SIAM J. Numer. Anal., 38 (2000), pp. 466.488.
|
19 |
A. Schatz and L. Wahlbin, Maximum norm estimates in the finite element method on plane polygonal domains, Part 1, Math. Comp., 32 (141), (1978) 73-109.
DOI
|
20 |
A. Schatz and L. Wahlbin, Maximum norm estimates in the finite element method on plane polygonal domains, Part 2 (refinements), Math. Comp., 33 (146), (1979) 465-492.
DOI
|
21 |
Z. Yosibash, Singularities in elliptic boundary value problems and elasticity and their connection with failure initiation, Interdisciplinary Applied Mathematics, 37. Springer, New York, 2012.
|
22 |
Ch. Schwab, p- and hp-Finite Element Methods, Oxford University Press, Oxford, 1998.
|
23 |
B. A. Szabo and I. Babuska, Finite Element Analysis, John Wiley & Sons, New York, 1991.
|
24 |
A. Quarteroni and A. Valli, Numerical Approximation of Partial Differential Equations, Springer-Verlag, Berlin, Germany, 1994.
|