1 |
R.B. Kellogg, Higher order singularities for interface problems, The mathematical foundations of the FEM with appl. to PDE, Acad. Press, 1972, 589-602.
|
2 |
N. Kishore Kumar, Nonconforming spectral element method for elasticity interface problems, Journal of Applied Mathematics and Informatics 32 (2014), 761-781.
DOI
|
3 |
N. Kishore Kumar, P. Dutt and C.S. Upadyay, Nonconforming spectral/hp element methods for elliptic systems, Journal of Numer. Math. 17 (2009), 119-142.
DOI
|
4 |
N. Kishore Kumar and G. Naga Raju, Least-squares hp/spectral element method for elliptic problems, Applied Numerical Mathematics 60 (2010), 38-54.
DOI
|
5 |
N. Kishore Kumar and G. Naga Raju, Nonconforming least-squares method for elliptic partial differential equations with smooth interfaces, Journal of Scientific Computing 53 (2012), 295-319.
DOI
|
6 |
V.A. Kondratiev, The smoothness of a solution of Dirichlet's problem for second order elliptic equations in a region with a piecewise smooth boundary, Differential' nye Uraneniya, 6 (1970), 1831-1843 (and Differential Equations, 6, 1392-1401).
|
7 |
Z. Li and K. Ito, The immersed interface method: Numerical solutions of PDEs involving interfaces and irregular domains, Frontiers Appl. Math. 33, SIAM, Philadelphia, 2006.
|
8 |
T.R. Lucas and H.S. Oh, The method of auxiliary mapping for the finite element solutions of elliptic problems containing singularities, Jour. of Comp. Phy. 108 (1993), 327-342.
DOI
|
9 |
S. Nicaise, Singularities in interface problems, Problems and Methods in Mathematical Physics, Springer Fachmedian Wiesbaden, 1994, 130-137.
|
10 |
M. Petzoldt, Regularity results for Laplace interface problems in two dimensions, Zeitschrift Fur Analysis and Ihre Anwendungen 20 (2001), 431-455.
DOI
|
11 |
H.S. Oh and I. Babuska, The p version of the finite element method for the elliptic boundary value problems with interfaces, Comp. Meth. in Appl. Mech. and Eng. 97 (1992), 211-231.
DOI
|
12 |
S.K. Tomar, h-p Spectral element method for elliptic problems on non-smooth domains using parallel computers, Computing 78 (2006), 117-143.
DOI
|
13 |
Ch. Schwab, p and h-p finite element methods, Clarendor Press, Oxford.
|
14 |
Y. Cao and M.D. Gunzburger, Least-square finite element approximations to solutions of interface problems, SIAM. J. Numer. Anal. 35 (1998), 393-405.
DOI
|
15 |
I. Babuska and B. Guo, On regularity of the solutions of elliptic problems with piecewise analytic data, part I: boundary value problems or linear elliptic equation of second order, SIAM J. Math. Anal. 19 (1988), 172-203.
DOI
|
16 |
I. Babuska and B. Guo, On the regularity of interface problem in terms of countably normed spaces.
|
17 |
I. Babuska, The finite element method for elliptic equations with discontinuous coeffcients, Computing 5 (1970), 207-213.
DOI
|
18 |
J.W. Barrett and C.M. Elliott, Fitted and unfitted finite element methods for elliptic equations with smooth interfaces, IMA Journal of Numer. Anal. 7 (1987), 283-300.
DOI
|
19 |
J.H. Bramble and J.T. King, A finite element method for interface problems in domains with smooth boundaries and interfaces, Adv. Com. Math. 6 (1996), 109-138.
DOI
|
20 |
P. Dutt, N. Kishore Kumar and C.S. Upadhyay, Nonconforming h-p spectral element methods for elliptic problems, Proc. Indian Acad. Sci (Math. Sci.) 117 (2007), 109-145.
DOI
|
21 |
P. Dutt, P. Biswas and G. Naga Raju, Preconditioners for spectral element methods for elliptic and parabolic problems, J. Comput. Appl. Math. 215 (2008), 152-166.
DOI
|
22 |
P. Grisvard, Elliptic problems in nonsmooth domain, Pitman Publishing Inc., Pitman 1985.
|
23 |
B. Guo and H.S. Oh, The hp version of the finite element method for problems with interfaces, Int. J. Nume. Meth. Engg. 37 (1994), 1741-1762.
DOI
|
24 |
H. Hon and Z. Huang, The direct of lines for the numerical solutions of interface problems, Comm. Meth. Appl. Mech. Engrg. 171 (1999), 61-75.
DOI
|
25 |
R.B. Kellogg, Singularities in interface problems, Numerical Solution of Partial Differential Equations II, B. Hubbard, editor, Academic Press, New York, 1971.
|
26 |
R.B. Kellogg, On the Poisson equation with intersecting interfaces, Applicable Analysis 4 (1975), 101-129.
DOI
|