A splitting extrapolation for solving nonlinear elliptic equations with d-quadratic finite elements
Journal of Computational Physics
A Finite Element Splitting Extrapolation for Second Order Hyperbolic Equations
SIAM Journal on Scientific Computing
Developing Finite Element Methods for Maxwell's Equations in a Cole-Cole Dispersive Medium
SIAM Journal on Scientific Computing
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In this paper we study a class of Petrov--Galerkin solutions that have global optimal convergence rates for linear Volterra integro-differential equations. These solutions also possess certain local and global superconvergence. Asymptotic expansions of the errors in these solutions are established which can be used to form higher order approximations by Richardson extrapolation and defect corrections. Several postprocessing techniques are introduced to enhance these solutions. As by-products, these higher order numerical approximations can be used to generate a posteriori error estimators. Representative numerical results are also provided.