A Finite Element Splitting Extrapolation for Second Order Hyperbolic Equations

Splitting extrapolation is an efficient technique for solving large scale scientific and engineering problems in parallel. This article discusses a finite element splitting extrapolation for second order hyperbolic equations with time-dependent coefficients. This method possesses a higher degree of parallelism, less computational complexity, and more flexibility than Richardson extrapolation while achieving the same accuracy. By means of domain decomposition and isoparametric mapping, some grid parameters are chosen according to the problem. The multiparameter asymptotic expansion of the d-quadratic finite element error is also established. The splitting extrapolation formulas are developed from this expansion. An approximation with higher accuracy on a globally fine grid can be computed by solving a set of smaller discrete subproblems on different coarser grids in parallel. Some a posteriori error estimates are also provided. Numerical examples show that this method is efficient for solving discontinuous problems and nonlinear hyperbolic equations.