
An adaptive highorder unfitted finite element method for elliptic interface problems
We design an adaptive unfitted finite element method on the Cartesian me...
read it

Analysis of finite element approximations of Stokes equations with nonsmooth data
In this paper we analyze the finite element approximation of the Stokes ...
read it

Hierarchical a posteriori error estimation of BankWeiser type in the FEniCS Project
In the seminal paper of Bank and Weiser [Math. Comp., 44 (1985), pp.283...
read it

Frequencyexplicit a posteriori error estimates for finite element discretizations of Maxwell's equations
We consider residualbased a posteriori error estimators for Galerkinty...
read it

A posteriori error analysis for a Lagrange multiplier method for a Stokes/Biot fluidporoelastic structure interaction model
In this work we develop an a posteriori error analysis of a conforming m...
read it

Goaloriented error estimation and adaptivity in MsFEM computations
We introduce a goaloriented strategy for multiscale computations perfor...
read it

An a posteriori error estimate of the outer normal derivative using dual weights
We derive a residual based aposteriori error estimate for the outer nor...
read it
Reliability and efficiency of DWRtype a posteriori error estimates with smart sensitivity weight recovering
We derive efficient and reliable goaloriented error estimations, and devise adaptive mesh procedures for the finite element method that are based on the localization of a posteriori estimates. In our previous work [SIAM J. Sci. Comput., 42(1), A371–A394, 2020], we showed efficiency and reliability for error estimators based on enriched finite element spaces. However, the solution of problems on a enriched finite element space is expensive. In the literature, it is well known that one can use some higherorder interpolation to overcome this bottleneck. Using a saturation assumption, we extend the proofs of efficiency and reliability to such higherorder interpolations. The results can be used to create a new family of algorithms, where one of them is tested on three numerical examples (Poisson problem, pLaplace equation, NavierStokes benschmark), and is compared to our previous algorithm.
READ FULL TEXT
Comments
There are no comments yet.