We study numerical approximations for geometric evolution equations arising as gradient flows for energy functionals that are quadratic in the principal curvatures of a two-dimensional surface. Beside the well-known Willmore and Helfrich flows we will also consider flows involving the Gaussian curvature of the surface. Boundary conditions for these flows are highly nonlinear, and we use a varia...

In this paper, a fully discrete stabilized discontinuous Galerkin method is proposed to solve the Biot's consolidation problem. The existence and uniqueness of the finite element solution are obtained. The stability of the fully discrete solution is discussed. The corresponding error estimates for the approximation of displacement and pressure in a mesh dependent norm are obtained. The error es...

This paper presents a comparative study on the newly introduced weak Galerkin finite element methods (WGFEMs) with the widely accepted discontinuous Galerkin finite element methods (DGFEMs) and the classical mixed finite element methods (MFEMs) for solving second-order elliptic boundary value problems. We examine the differences, similarities, and connection among these methods in scheme formul...

H1-Galerkin mixed finite element methods are analysed for parabolic partial integrodifferential equations which arise in mathematical models of reactive flows in porous media and of materials with memory effects. Depending on the physical quantities of interest, two methods are discussed. Optimal error estimates are derived for both semidiscrete and fully discrete schemes for problems in one sp...