## The L 2 - 1 σ scheme is applied for the discretization of time fractional derivative on graded meshes and anisotropic finite element method (FEM) is employed for the spatial discretization.

Convergence analysis of the anisotropic FEM for 2D time fractional variable coefficient diffusion equations on graded meshes

## Therefore, in order to improve the convergence order, we discrete the Caputo time fractional derivative by a new \begin{document}$L1-2$\end{document} format on graded meshes, while the spatial derivative term is approximated by the classical central difference scheme on uniform meshes.

A fast high order method for time fractional diffusion equation with non-smooth data

## It is shown that optimal convergence rates can be obtained by using special graded meshes.

Block boundary value methods for linear weakly singular Volterra integro-differential equations

## The existence and uniqueness of collocation solutions are proved under two special graded meshes.

Collocation methods for third-kind Volterra integral equations with proportional delays

10.1016/J.APNUM.2021.05.006

## In this paper, we introduce a multi-domain Muntz-polynomial spectral collocation method with graded meshes for solving second kind Volterra integral equations with a weakly singular kernel.

A multi-domain spectral collocation method for Volterra integral equations with a weakly singular kernel

10.1515/CMAM-2020-0158

## So, we use the L1 scheme on graded meshes for time discretization.

A Low-Dimensional Compact Finite Difference Method on Graded Meshes for Time-Fractional Diffusion Equations

10.1016/J.APNUM.2020.09.003

## Among them, some popular methods were constructed by using the graded meshes due to the solution with low temporal regularity.

A numerical method for two-dimensional multi-term time-space fractional nonlinear diffusion-wave equations

10.1016/j.cam.2020.113156

## Moreover, for a short-memory process, the optimal strong convergence order of the method with distributions under uniform and graded meshes is discussed.

Strong convergence analysis for Volterra integro-differential equations with fractional Brownian motions

10.1016/j.apnum.2020.11.006

## For solutions with singular behaviour near t = 0 caused by the weakly singular kernels, we prove optimal algebraic convergence rates for the h-version of the discontinuous Galerkin approximations on graded meshes.

An hp-version of the discontinuous Galerkin time-stepping method for Volterra integral equations with weakly singular kernels

## For the weighted finite element method an absolute error value is by one or two orders of magnitude less than for the approximate generalized solution obtained by the FEM with graded meshes in the overwhelming majority of nodes.

Comparative analysis of the weighted finite element method and FEM with mesh refinement

10.1007/s42967-021-00142-5

## Both h- and k-dependency are investigated tackling two- and three-dimensional problems on standard meshes and graded meshes.

p-Multilevel preconditioners for HHO discretizations of the Stokes equations with static condensation

10.1016/J.APNUM.2018.11.014

## To overcome this difficulty, we use the L1 scheme on graded meshes in time, such that considered time steps are very small near the origin which compensate the singularity of the solution.

Reduced spline method based on a proper orthogonal decomposition technique for fractional sub-diffusion equations

10.1007/S10915-019-00943-0

## Iterative processes or corrected schemes become dispensable by the use of the Newton linearized method and graded meshes in the temporal direction.

Linearized Galerkin FEMs for Nonlinear Time Fractional Parabolic Problems with Non-smooth Solutions in Time Direction

## We address this issue, and in particular we derive error estimates for the Lagrange finite element solutions on both quasi-uniform and graded meshes.

On the Convergence in H1-Norm for the Fractional Laplacian

10.1016/J.CAM.2019.01.031

## A second-order accurate numerical method with graded meshes is proposed and analyzed for an evolution equation with a weakly singular kernel.

A second-order accurate numerical method with graded meshes for an evolution equation with a weakly singular kernel

10.1016/j.cam.2018.08.029

## In this paper, we investigate the local superconvergence of the discontinuous Galerkin (DG) solutions on quasi-graded meshes for nonlinear delay differential equations with vanishing delay.

Superconvergence of discontinuous Galerkin methods for nonlinear delay differential equations with vanishing delay

10.1016/j.amc.2019.06.023

## To deal with the weak singularity caused by the fractional derivative that the solution has in the initial layer, the well-known L1 scheme on graded meshes has been used for time discretization.

A finite difference scheme on graded meshes for time-fractional nonlinear Korteweg-de Vries equation

10.1515/cmam-2019-0011

## In this paper we investigate multigrid methods for a quad-curl problem on graded meshes.

Multigrid Methods Based on Hodge Decomposition for a Quad-Curl Problem