L^∞(L²)andL^∞(L^∞)error estimates for mixed methods for integro-differential equations of parabolic type

Abstract

Abstract. Error estimates in L2 ), Ω in R 2 , are derived for a mixed finite element method for the initial-boundary value problem for integro-differential equation

Weak Galerkin finite element methods for linear parabolic integro-differential equations

“…For earlier work on numerical solutions of parabolic integro-differential equations, see for example, [1][2][3][4][5][6][7][8][9]. In recent years, several finite element/volume techniques for equations above have been studied, including mixed finite element methods [10][11][12], expanded mixed finite element methods [13,14], expanded mixed covolume methods [15], h p -local discontinous Galerkin methods [16], discontinuous mixed covolume methods [17], and least-squares finite element methods [18].…”

A Mixed Covolume Method For The Pseudo-Parabolic Integro-Differential Equation On Triangular Grids

“…Throughout this paper, we use C (without or with subscript) to denote a generic constant independent of the discretization parameters, which has different values in different appearances. We also adopt the standard definitions and notations of Sobolev spaces and their full norms and seminorms in [1], [5], [9].…”

Split least‐squares finite element methods for non‐Fickian flow in porous media

“…References [5] and [6] have considered the finite element methods, and [7] have considered the finite volume methods for this problem. Jiang [8] have considered mixed element methods for this problem when A , B are proportional to a unit matrix, and Euring et al [1] and [2] have considered the L 2 ‐error estimate and L ∞ ‐error estimate of mixed element methods for this problem in a general case. The advantage of mixed element is that the approximations to u and σ can be obtained simultaneously.…”

“…References [5] and [6] have considered the finite element methods, and [7] have considered the finite volume methods for this problem. Jiang [8] have considered mixed element methods for this problem when A, B are proportional to a unit matrix, and Euring et al…”