Arbitrary High-Order Finite Element Schemes and High-Order Mass Lumping

Butcher J.C. (2003): Numerical Methods for Ordinary Differential Equations. Chichester: John Wiley and Sons.10.1002/0470868279Search in Google Scholar

Chin-Joe-Kong M.J.S., Mulder W.A. and Van Veeldhuizen M. (1999): Higher-order triangular and tetrahedral finite elements with mass lumping for solving the wave equation. Journal of Engineering Mathematics Vol. 35, No. 4, pp. 405-426.10.1023/A:1004420829610Search in Google Scholar

Ciarlet P.G. (1978): The Finite Element Method for Elliptic Problems. North-Holland, Amsterdam.10.1115/1.3424474Search in Google Scholar

Cohen G. (2002): Higher Order Numerical Method for Transient Wave Equations. Berlin: Springer-Verlag.10.1007/978-3-662-04823-8Search in Google Scholar

Cohen G., Joly P., Roberts J.E. and Tordjman N. (2001): Higher order triangular finite element with mass lumping for the wave equation. SIAM Journal on Numerical Analysis, Vol. 38, No. 6, pp. 2047-2078.10.1137/S0036142997329554Search in Google Scholar

Cohen G., Joly P. and Tordjman N. (1994): Higher-order finite elements with mass lumping for the 1D wave equation. Finite Elements in Analysis and Design, Vol. 16, No. 3-4, pp. 329-336.10.1016/0168-874X(94)90075-2Search in Google Scholar

Cohen G., Joly P. and Tordjman N. (1993): Construction and analysis of higher order finite elements with mass lumping for the wave equation, In: Proceedings of the Second International Conference on Mathematical and Numerical Aspects of Wave Propagation Phenomena, SIAM, Philadelphia, pp. 152-160.Search in Google Scholar

Dumbser M. (2005): Arbitrary High Order Schemes for the Solution of Hyperbolic Conservation Laws in Complex Domains. Ph.D. thesis, Stuttgart University.Search in Google Scholar

Fix G.J. (1972): Effect of quadrature errors in the finite element approximation of steady state, eigenvalue and parabolic problems, In: The Mathematical Foundations of the Finite Element Method with Applications to the Partial Differential Equations, (A.K. Aziz, Ed.), New York: Academic Press, pp. 525-556.Search in Google Scholar

Lax P.D. and Wendroff B. (1960): Systems of conservation laws. Communications on Pure Applied Mathematics, Vol. 13, pp. 217-237.10.1002/cpa.3160130205Search in Google Scholar

Mulder W.A. (1996): A comparison between higher-order finite elements and finite differences for solving the wave equation, In: Proceedings of the Second ECCOMAS Conference Numerical Methods in Engineering, (J.-A. Désidéri, P. Le Tallec, E. Oñate, J. Périaux and E. Stein, Eds.), Chichester: John Wiley and Sons, pp. 344-350Search in Google Scholar

Tordjman N. (1995): Eléments finis d'ordre élevés avec condensation de masse pour l'équation des onde. Ph.D. Thesis, Université Paris IX Dauphine, Paris.Search in Google Scholar

Titarev V.A. and Toro E.F. (2002): ADER: Arbitrary high order Godunov approach.Journal of Scientific Computing, Vol. 17, No. 1-4, pp. 609-618.10.1023/A:1015126814947Search in Google Scholar