AP 1-nonconforming quadrilateral finite element is introduced for second-order elliptic
problems in two dimensions. Unlike the usual quadrilateral nonconforming finite elements …

We present the nonconforming virtual element method for linear elasticity problems in the
pure displacement formulation. This method is uniformly convergent for the nearly …

This article proposes a nonconforming immersed finite element (IFE) method for solving
planar elasticity interface problems with structured (or Cartesian) meshes even if the …

Residual-based a posteriori error estimates were derived within one unifying framework for
lowest-order conforming, nonconforming, and mixed finite element schemes in Carstensen …

The objective of the present study is to show that the numerical instability characterized by
checkerboard patterns can be completely controlled when non‐conforming four‐node finite …

In science and engineering, many simulations are carried out over domains consisting of
multiple materials separated by curves/surfaces. If partial differential equations (PDEs) are …

The numerical approximation of partial differential equations coming from physical and
engineering modeling is often a challenging task. Most often these partial differential …

Topology optimization of a compliant mechanism under pressure input is presented by
treating void regions with incompressible hydrostatic fluid. Since an input force is not …

This thesis is concerned with new numerical and algorithmic tools for flows with pressure
and shear dependent viscosity together with the necessary background of the generalized …

We consider finite-element methods based on simplices to solve the problem of nearly
incompressible elasticity. Two different approaches based, respectively, on dual meshes …