Asymptotic error expansion and richardson extrapolation for linear fine elements
Numerische Mathematik
Extrapolation of the iterated—collocation method for integral equations of the second kind
SIAM Journal on Numerical Analysis
Journal of Scientific Computing
Implicit extrapolation methods for multilevel finite element computations
SIAM Journal on Scientific Computing - Special issue on iterative methods in numerical linear algebra; selected papers from the Colorado conference
A Complete Convergence and Stability Theory for a Generalized Richardson Extrapolation Process
SIAM Journal on Numerical Analysis
Implicit Extrapolation Methods for Variable Coefficient Problems
SIAM Journal on Scientific Computing
Petrov--Galerkin Methods for Linear Volterra Integro-Differential Equations
SIAM Journal on Numerical Analysis
The Richardson Extrapolation Process with a Harmonic Sequence of Collocation Points
SIAM Journal on Numerical Analysis
Journal of Computational and Applied Mathematics
Mechanical quadrature methods and their extrapolation for solving first kind Abel integral equations
Journal of Computational and Applied Mathematics
One-sided finite-difference approximations suitable for use with Richardson extrapolation
Journal of Computational Physics
Journal of Computational and Applied Mathematics
International Journal of Computer Mathematics - Splitting Methods for Differential Equations
A splitting extrapolation for solving nonlinear elliptic equations with d-quadratic finite elements
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational and Applied Mathematics
Extrapolation discontinuous Galerkin method for ultraparabolic equations
Journal of Computational and Applied Mathematics
Advances in Computational Mathematics
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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.