This book is the third volume of a three-part textbook suitable for graduate coursework,
professional engineering and academic research. It is also appropriate for graduate flipped …

We establish the well-posedness of an hp-version time-stepping discontinuous Galerkin
method for the numerical solution of fractional superdiffusion evolution problems. In …

We present an hp version of the continuous Petrov--Galerkin (CPG) finite element method
for linear Volterra integro-differential equations with smooth and nonsmooth kernels. We …

We introduce a multistep Legendre--Gauss spectral collocation method for the nonlinear
Volterra integral equations of the second kind. This method is easy to implement and …

We develop and analyze an hp-version of the discontinuous Galerkin time-stepping method
for linear Volterra integral equations with weakly singular kernels. We derive a priori error …

The aim of this paper is to develop an hp-version a posteriori error analysis for the time
discretization of parabolic problems by the continuous Galerkin (cG) and the discontinuous …

We introduce and analyze a very simple but efficient postprocessing technique for improving
the accuracy of the continuous Galerkin (CG) time stepping method for nonlinear first-order …

The aim of this paper is to propose and analyze two postprocessing techniques for
improving the accuracy of the C1-and C0-continuous Galerkin (CG) time stepping methods …

We introduce and analyze an-version-continuous Petrov–Galerkin (CPG) method for
nonlinear initial value problems of second-order ordinary differential equations. We derive a …

The hp version of the continuous Petrov-Galerkin time stepping method is analyzed for
nonlinear initial value problems. An L∞-error bound explicit with respect to the local …