A Discontinuous Mixed Covolume Method For Fourth-order Semilinear Evolution Equations

Consider the initial boundary value problems of the following fourth-order semi-linear evolution equation The problems satisfy the initial condition For the boundary conditions, we consider the following two cases The above initial boundary problems are discretized by a discontinuous mixed co-volume method. The semi-discrete and full-discrete schemes are formulated and analyzed. In the case of boundary condition I, error estimates of w in L2-normal, and optimal error estimate of u in H1-normal are derived. In the case of boundary condition II, we obtain the optimal error estimates of u and w in L2-normal, and optimal error estimate of u in H1-normal. Finally, we present numerical experi-ments which validate the theoretical analysis and illustrate the effectiveness of the discontinuous mixed covolume method.