Sentence examples for by mixed element methods from inspiring English sources

For example, in 1978 (see [22]), Brezzi and Raviart studied fourth order elliptic equations by mixed element methods.

To overcome this disadvantage of mixed element methods, Rui [5] gave some split least-squares finite element procedures and the convergence analysis with optimal accuracy.

Recently, in [13, 14] we did some primary work on a priori error estimates for nonlinear parabolic optimal control problems by mixed finite element methods.

The a posteriori error estimates for the semilinear parabolic optimal control problems by mixed finite element methods seem to be new.

The priori error estimates for the elliptic optimal control problems by variational discretization and mixed finite element methods seem to be new.

In [16], we derived a posteriori error estimates for linear parabolic optimal control problems by the lowest order Raviart-Thomas mixed finite element methods.

With the intermediate errors, we can decompose the errors as follows: p − p h = p − p ( u h ) + p ( u h ) − p h : = ϵ 1 + ε 1, y − y h = y − y ( u h ) + y ( u h ) − y h : = r 1 + e 1, q − q h = q − q ( u h ) + q ( u h ) − q h : = ϵ 2 + ε 2, z − z h = z − z ( u h ) + z ( u h ) − z h : = r 2 + e 2. By using the standard results of mixed finite element methods [26], we have the following results.

We introduce a new family of mixed finite elements for incompressible nonlinear elasticity – compatible-strain mixed finite element methods (CSFEMs).

In this article, we investigate a priori error estimates for the optimal control problems governed by elliptic equations using higher order variational discretization and mixed finite element methods.

In this paper, we consider the mixed finite element methods for quadratic optimal control problems governed by convective diffusion equations.

In this paper we derive a posteriori error estimates of mixed finite element methods for general optimal control problems governed by integro-differential equations.