Robust and Local Optimal A Priori Error Estimates for Interface Problems with Low Regularity: Mixed Finite Element Approximations

Discontinuous Finite Element Methods for Interface Problems: Robust A Priori and A Posteriori Error Estimates

Abstract. For elliptic interface problems in two and three dimensions, this paper studies a priori and residual-based a posteriori error estimations for the Crouzeix–Raviart nonconforming and the discontinuous Galerkin finite element approximations. It is shown that both the a priori and the a posteriori error estimates are robust with respect to the diffusion coefficient, i.e., constants in th...

A Priori Error Estimates for Mixed Finite Element Approximations of the Acoustic Wave Equation

In this paper we derive optimal a priori L∞(L2) error estimates for mixed finite element displacement formulations of the acoustic wave equation. The computational complexity of this approach is equivalent to the traditional mixed finite element formulations of the second order hyperbolic equations in which the primary unknowns are pressure and the gradient of pressure. However, the displacemen...

Optimal a priori estimates for interface problems

Sharp estimates for finite element approximations to elliptic problems with Neumann boundary data of low regularity

Consider a second order homogeneous elliptic problem with smooth coefficients, Au = 0, on a smooth domain, Ω, but with Neumann boundary data of low regularity. Interior maximum norm error estimates are given for C0 finite element approximations to this problem. When the Neumann data is not in L1(∂Ω), these local estimates are not of optimal order but are nevertheless shown to be sharp. A method...

A priori error estimates for higher order variational discretization and mixed finite element methods of optimal control problems

* Correspondence: zulianglux@126. com College of Civil Engineering and Mechanics, Xiangtan University, Xiangtan 411105, PR China Full list of author information is available at the end of the article Abstract 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 elem...