A feasibility study for discontinuous Galerkin discretization with embedded Dirichlet boundary condition

Applied Numerical Mathematics

Volumn 51, Issue 2-3, 2004, Pages 361-383

  Van Raalte, M H ^a,b  

^a UNIVERSITY OF AMSTERDAM   (Netherlands)

^b CWI   (Netherlands)

Author keywords

Discontinuous Galerkin (DG) methods; Embedded boundary; Structured grid

Indexed keywords

BOUNDARY CONDITIONS; BOUNDARY VALUE PROBLEMS; FINITE ELEMENT METHOD; MATHEMATICAL MODELS; PARTIAL DIFFERENTIAL EQUATIONS; POLYNOMIALS; PROBLEM SOLVING; TENSORS;

DIRICHLET BOUNDARY CONDITIONS; DISCONTINUOUS GALERKIN (DG) METHODS; EMBEDDED BOUNDARIES; STRUCTURED GRIDS;

GALERKIN METHODS;

EID: 5144223344     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apnum.2004.06.016     Document Type: Article

References (17)

1. D.N. Arnold, F. Brezzi, B. Cockburn, D. Marini, Unified analysis of discontinuous Galerkin methods for elliptic problems, SIAM J Numer. Anal. 39 (2002) 1749-1779.
2. C.E. Baumann, J.T. Oden, A discontinuous hp-finite element method for convection diffusion problems, Comput. Methods Appl. Mech. Engrg. 175 (1999) 311-341.
3. C.E. Baumann, An hp-Adaptive Discontinuous Finite Element Method for Computational Fluid Dynamics, Ph.D. Thesis, The University of Texas at Austin, Austin, TX, 1997.
4. R. Cortez, M. Minion, The Blob projection method for immersed boundary problems, J. Comput. Phys. 161 (2000) 428-453.
5. P.W. Hemker, A singularly perturbed model problem for numerical computation, J. Comput. Appl. Math. 76 (1997) 277-285.
6. P.W. Hemker, W. Hoffmann, M.H. van Raalte, Discontinuous Galerkin discretization with embedded boundary conditions, Comput. Methods Appl. Math. 3 (2003) 135-158.
7. P.W. Hemker, M.H. van Raalte, Fourier two-level analysis for higher dimensional discontinuous Galerkin discretization, Technical Report MAS-R0227, CWI, Amsterdam, November 2002, Comput. Vis. Sci., submitted for publication.
8. D.W. Hewett, C.S. Kucny, The dielectric boundary condition for the embedded curved boundary (ECB) method, Technical Report UCRL-JC-129703, Lawrence Livermore Nat. Lab., 1998, presented at the 16th International Conference on the Numerical Simulation of Plasmas, February 1998, Santa Barbara, CA.
9. P. Houston, C. Schwab, E. Süli, Discontinuous hp-finite element methods for advection-diffusion problems, Technical Report No. 2000-07, ETHZ, Zürich, 2000.
10. C.S. Kueny, Embedded curved boundaries and adaptive mesh refinement, Technical Report UCRL-JC-129729, Lawrence Livermore Nat. Lab., Livermore, CA, 1998.
11. J. Nitsche, Über ein Variationsprinzip zur Lösung von Dirichlet Problemen bei Verwendung von Teilräumen die keinen Randbedingungen unterworfen sind, Abh. Math. Sem. Univ. Hamburg 36 (1971) 9-15.
12. J.T. Oden, I. Babuška, C.E. Baumann, A discontinuous hp finite element method for diffusion problems, J. Comput. Phys. 146 (1998) 491-519.
13. C.S. Peskin, Numerical analysis of blood flow in the heart, J. Comput. Phys. 25 (1977) 220-252.
14. S. Prudhomme, F. Pascal, J.T. Oden, A.Romkes, Review of a priori error estimations for discontinuous Galerkin methods, TICAM Report 00-27, 2000.
15. J.F. Remacle, J.E. Flaherty, M.S. Shephard, An adaptive discontinuous Galerkin technique with an orthogonal basis applied to compressible flow problems, SIAM Rev. 45 (2003) 53-72.
16. E. Süli, C. Schwab, P. Houston, hp-DGFEM for partial differential equations with non-negative characteristic form, in: B. Cockburn, G.E. Karniadakis, C.-W. Shu (Eds.), Discontinuous Galerkin Methods. Theory, Computation and Applications, Lecture Notes in Comput. Sci. Engrg., vol. 11, Springer, New York, 2000, pp. 221-230.
17. C. Tu, C.S. Peskin, Stability and instability in the computation of flows with moving immersed boundaries: A comparison of three methods, SIAM J. Sci. Statist. Comput. 13 (1992) 1361-1376.