Regularization Techniques for Numerical Approximation of PDEs with Singularities

Journal of Scientific Computing

Volumn 19, Issue 1-3, 2003, Pages 527-552

  Tornberg, Anna Karin ^a   Engquist, Björn ^b,c  

^a NEW YORK UNIVERSITY   (United States)

^b PRINCETON UNIVERSITY   (United States)

^c UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Discontinuous coefficients; Local regularization; Moment conditions; Singular source terms

Indexed keywords

LOCAL REGULARIZATION; MOMENT CONDITIONS;

APPROXIMATION THEORY; BOUNDARY CONDITIONS; COMPUTATIONAL METHODS; COMPUTER SIMULATION; CONVERGENCE OF NUMERICAL METHODS; DIFFERENTIAL EQUATIONS; FUNCTIONS; INTERPOLATION; MULTIPHASE FLOW; PROBLEM SOLVING;

PARTIAL DIFFERENTIAL EQUATIONS;

EID: 0346009119     PISSN: 08857474     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1025332815267     Document Type: Article

References (18)

1. Abarbanel, S., Gottlieb, D., and Tadmor, E. (1986). Spectral Methods for Discontinuous Problems. Proceedings of the 1985 Conference on Numerical Method for Fluid Dynamics II, Clarendon Press, Oxford, pp. 101-135.
2. Beale, J. T., and Majda, A. (1982). Vortex methods. II: Higher order accuracy in two and three dimensions. Math. Comput. 39, 29-52.
3. Bensoussan, A., Lions, J.-L., and Papanicolaou, G. (1978). Asymptotic Analysis for Periodic Structures, North-Holland.
4. Beyer, R. P., and LeVeque, R. J. (1992). Analysis of a one-dimensional model for the immersed boundary method. SIAM J. Numer. Anal. 29, 332-364.
5. Beylkin, G. (1995). On the fast Fourier transform of functions with singularities. Appl. Comput. Harmon. A. 2, 363-381.
6. Ditkowski, A., Dridi, K., and Hesthaven, J. S. (2001). Convergent Cartesian grid methods for Maxwell's equations in complex geometries. J. Comput. Phys. 170, 39-80.
7. Glowinski, R., Pan, T. W., Hesla, T. I., and Joseph, D. D. (1999). A distributed Lagrange multiplier/fictitious domain method for particulate flows. Int. J. Multiphas. Flow 25, 755-794.
8. Kreiss, H.-O., and Lorenz, J. (1989). Initial-Boundary Value Problems and the Navier-Stokes Equations, Academic Press, New York.
9. Ledfelt, G. (2001). Hybrid Time-Domain Methods and Wire Models for Computational Electromagnetics, TRITA-NA-0106, KTH.
10. LeVeque, R. J., and Li, Z. (1994). The immersed interface method for elliptic equations with discontinuous coefficients and singular sources. SIAM J. Numer. Anal. 31, 1019-1044.
11. Peskin, C. S. (1977). Numerical analysis of blood flow in the heart. J. Comput. Phys. 25, 220-252.
12. Peskin C. S. (2002). The immersed boundary method. Acta Numerica 11, 479-517.
13. Sussman, M., Smereka, P., and Osher, S. (1994). A level set approach for computing solutions to incompressible two-phase flow. J. Comput. Phys. 114, 146-159.
14. Taflove, A., and Hagness, S. C. (2000). Computational Electrodynamics: The Finite-Difference Time Domain Method, 2nd ed., Artech House, Norwood, Massachusetts.
15. Tornberg A.-K. (2000). Interface tracking methods with applications to multiphase flows. Ph.D. thesis, Department of Numerical Analysis and Computer Science, Royal Institute of Technology (KTH), Stockholm, Sweden. ISBN 91-7170-558-9, TRITA-NA 0010.
16. Tornberg, A.-K. (2002). Multi-dimensional quadrature of singular and discontinuous functions. BIT 42, 644-669.
17. Tornberg, A.-K., and Engquist, B. (2000). A finite element based level set method for multiphase flow applications. Comput. Vis. Sci. 3, 93-101.
18. Unverdi, S. O., and Tryggvason, G. (1992). A front-tracking method for viscous incompressible, multi-fluid flows. J. Comput. Phys. 100, 25-37.