Weak Galerkin Finite Element Method For Two Classes Of Time Fractional Diffusion Equations

The weak Galerkin finite element method is the extension of the classical finite element method.This method is used for the division of arbitrary polygons and polyhedra in a region.It is a numerical method to solve partial differential equa-tions based on fragment polynomials.It has been widely used in various partial differential equations.In this dissertation,we study the weak Galerkin finite ele-ment method of single-time fractional diffusion equation and multi-time fractional diffusion equation,and obtains a fully discrete finite element scheme,~2mode and~1mode error estimates.There are differences for the two classes of time fraction-al diffusion equations.For a single time fractional diffusion equation,we select the Dirichlet homogeneous boundary conditions,apply a uniform grid to obtain a fully discrete finite element scheme,and prove the existence and uniqueness,moreover,we prove the stability and estimate the error.In the numerical example,we se-lect different time fractional order to obtain the error convergence of the diffusion equation under the homogeneous Dirichlet boundary conditions.For the single time fractional diffusion equation,we select the Dirichlet homogeneous boundary conditions,apply a grad grid to obtain a fully discrete finite element scheme,and prove the stability,moreover,we estimate the error.In the numerical example,we select different time fractional order to obtain the error convergence of single time fractional diffusion equation under the homogeneous Dirichlet boundary con-ditions.For the multi-time fractional diffusion equation,we select the Dirichlet homogeneous boundary conditions,apply a uniform grid to obtain a fully discrete finite element scheme,and prove the existence and uniqueness,moreover,we prove the stability and estimate the error.In the numerical example,we select different time fractional order to obtain the error convergence of the multi-time fraction-al diffusion equation under the homogeneous Dirichlet boundary conditions.This dissertation gives numerical examples to verify the correctness of the theoretical derivation for each format.