Since the nonconforming P1 finite element method for the Stokes equations was introduced
by M. Crouzeix and PA Raviart in 1973, there have been many advances in the finite …

A conforming discontinuous Galerkin (CDG) C 0-P k finite element method is introduced for
solving the biharmonic equation on triangular and tetrahedral meshes. AC 0-P k finite …

This paper introduces a new family of mixed finite elements for solving a mixed formulation
of the biharmonic equations in two and three dimensions. The symmetric stress σ=−∇ 2 u is …

We analyse an energy minimisation problem recently proposed for modelling smectic-A
liquid crystals. The optimality conditions give a coupled nonlinear system of partial …

For the first biharmonic problem a mixed variational formulation is introduced which is
equivalent to a standard primal variational formulation on arbitrary polygonal domains …

In this paper, we apply the weakly over-penalized symmetric interior penalty method to solve
some variational inequalities which include the Signorini problem and the obstacle problem …

A unified framework for fourth-order semilinear problems with trilinear nonlinearity and
general sources allows for quasi-best approximation with lowest-order finite element …

The popular (piecewise) quadratic schemes for the biharmonic equation based on triangles
are the nonconforming Morley finite element, the discontinuous Galerkin, the C 0 interior …

In this paper, we propose and analyze a new weakly over-penalized symmetric interior
penalty (WOPSIP) discontinuous Galerkin (DG) scheme for the Stokes equations. The …

An abstract property (H) is the key to a complete a priori error analysis in the (discrete)
energy norm for several nonstandard finite element methods in the recent work [Lowest …