Analysis of second order finite volume element methods for pseudo-parabolic equations in three spatial dimensions (Q2474861)

The author is concerned with a finite volume element approximation of pseudo-parabolic equation of the form \[ u_t-\Delta u_t-\mu \Delta u=f(x,t)\text{ in }(0,1)^3\times(0,T], \] subject to boundary condition \(u=0\) on \(\partial\Omega\times (0,T]\), and \(u(x,0)=u_0(x)\) in \(\Omega\). Triquadratic elements are used as solution space to obtain a high order convergence rate. Based on some dual partition, an optimal error estimate in the \(H^1\)-norm of the second order accuracy is established. Numerical results are also presented and illustrate the efficiency of the method.