Unconditionally optimal error estimates of a linearized weak Galerkin finite element method for semilinear parabolic equations

In this paper, we consider the unconditionally optimal error estimates of the linearized backward Euler scheme with the weak Galerkin finite element method for semilinear parabolic equations. With the error splitting technique and elliptic projection, the optimal error estimates in L²-norm and the discrete H¹-norm are derived without any restriction on the time stepsize. Numerical results on both polygonal and tetrahedral meshes are provided to illustrate our theoretical conclusions.