Highly efficient H 1-Galerkin mixed finite element method (MFEM) for parabolic integro-differential equation

Asymptotic Expansions and Extrapolations ofH1-Galerkin Mixed Finite Element Method for Strongly Damped Wave Equation

“…In order to carry out the the extrapolation of H 1 -Galerkin MFEM, we also need the following conclusion proved in [13,25] …”

“…As to MFEM, [6,9,15] gave the asymptotic error expansions of the lowest rectangular Raviart-Thomas finite element so as to improve the approximation accuracy in L 2 (Ω) norm for second order elliptic problem, parabolic type integro-differential equation and eigenvalue problem with integral identities and Richardson extrapolation techniques. Moreover, [33] studied the extrapolation of the Nédélec finite element for Maxwell equation.[35] also investigated the asymptotic error expansions for the Stokes eigenvalue problem by Bernadi-Raugel finite element.However, to our best knowledge, there are few reports on the study of extrapolations of H 1 -Galerkin MFEM except for our early work [25]. In this paper, as an extension of [25], we first establish asymptotic expansions for the error between the H 1 -Galerkin MFE solution and the corresponding interpolation function of the exact solution with linear triangular finite element.…”

“…However, to our best knowledge, there are few reports on the study of extrapolations of H 1 -Galerkin MFEM except for our early work [25]. In this paper, as an extension of [25], we first establish asymptotic expansions for the error between the H 1 -Galerkin MFE solution and the corresponding interpolation function of the exact solution with linear triangular finite element.…”

Unconditional superconvergence analysis of an H1‐galerkin mixed finite element method for nonlinear Sobolev equations

“…To remove this restriction, an H 1 ‐Galerkin MFEM was proposed by Pani in , in which the approximation spaces can be chosen freely without the above restriction and the quasiuniformity of the meshes. Recently, such a method has been applied widely to many problems, such as integro‐differential equations and parabolic equations .…”