We review different techniques to enforce essential boundary conditions, such as the
(nonhomogeneous) Dirichlet boundary condition, within a discrete variational framework …

A residual‐type a posteriori error estimator is proposed and analyzed for a modified weak
Galerkin finite element method solving second‐order elliptic problems. This estimator is …

Purpose–The purpose of this paper is to present a simple meshless solution method for
challenging engineering problems such as those with high wave numbers or convection …

Fully computable upper bounds are developed for the discretisation error measured in the
natural (energy) norm for convection–reaction–diffusion problems in three dimensions. The …

We propose, analyze and test a new adaptive penalty scheme that picks the penalty
parameter ϵ element by element small where∇· uh is large. We start by analyzing and …

Numerical solution of convection-dominated problems requires special techniques to
suppress spurious oscillations in approximate solutions. Often, stabilized methods are …

An optimal adaptive multiscale finite element method (AMsFEM) for numerical solutions of
flow problems modelled by the Oldroyd B model is developed. Complex flows experience …

We derive computable a posteriori error estimates for a wide family of low-order conforming
and conforming stabilized finite element approximations for fluid flow problems. The …

Using the T-coercivity theory as advocated in [Chesnel, Ciarlet, T-coercivity and continuous
Galerkin methods: application to transmission problems with sign changing coefficients …

In this work, we derive a posteriori error estimates for discontinuous Galerkin finite element
method on polytopal mesh. We construct a reliable and efficient a posteriori error estimator …