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A discontinuous Galerkin method for the Rosenau equation. (English) Zbl 1145.65071
This paper is concerned with a posteriori error estimates for the Rosenau equation $$u_t+u_{xxxxt}=f(u)_x$$ in $\Omega\times (0,T]$ subject to the boundary conditions $u(x,t)=u_x(x,t)=0$ on $\partial\Omega\times (0,T]$ and $u(x,0)=u_0(x)$, $x\in\overline\Omega$. Here $\Omega=(0,1)$, $f(u)=-u-u^2$ and $T>0$. A posteriori estimates are obtained by using the discontinuous Galerkin method. The stability of the approximated solution is also discussed. Numerical results on a posteriori error and wave propagation are given, which are obtained by using various spatial and temporal meshes controlled automatically by a posteriori error.

MSC:
65M60Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (IVP of PDE)
65M12Stability and convergence of numerical methods (IVP of PDE)
65M15Error bounds (IVP of PDE)
35K55Nonlinear parabolic equations
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References:
[1] Ainsworth, M.; Oden, J. T.: A posteriori error estimation in finite element analysis. Comp. meth. Appl. mech. Eng. 142, 1-88 (1997) · Zbl 0895.76040
[2] Chung, S. K.; Ha, S. N.: Finite element Galerkin solutions for the rosenau equation. Appl. anal. 54, 39-56 (1994) · Zbl 0830.65097
[3] Chung, S. K.; Pani, A. K.: Numerical methods for the rosenau equation. Appl. anal. 77, 351-369 (2001) · Zbl 1021.65048
[4] Eriksson, K.; Johnson, C.: Adaptive finite element methods for parabolic problem IV: Nonlinear problems. SIAM J. Numer. anal. 32, 1729-1749 (1995) · Zbl 0835.65116
[5] Grasselli, M.; Perotto, S.; Saleri, F.: Space-time finite element approximation of Boussinesq equations. East-west J. Numer. math. 7, 283-306 (1999) · Zbl 0948.65100
[6] Lee, H. Y.; Ahn, M. J.: The convergence of the fully discrete solution for the rosenau equation. Comp. math. Appl. 32, 15-22 (1996) · Zbl 0857.65103
[7] Park, M. A.: Pointwise decay estimates of solutions of the generalized rosenau equation. J. of korean math. Soc. 29, 261-280 (1992) · Zbl 0808.35020
[8] Park, M. A.: On the rosenau equation in multidimensional space. Nonlinear anal., T.M.A. 21, 77-85 (1993) · Zbl 0811.35142
[9] Rosenau, P.: Dynamics of dense discrete systems. Prog. theoret. Phys. 79, 1028-1042 (1988)