A discontinuous Galerkin pressure correction numerical method for solving the incompressible Navier–Stokes equations is formulated and analyzed. We prove unconditional stability of proposed scheme. Convergence discrete velocity established by deriving a priori error estimates. Numerical results verify convergence rates.

A priori and a posteriori error estimates are derived for the numerical approximation of scalar and complex valued phase field models. Particular attention is devoted to the dependence of the estimates on a small parameter and to the validity of the estimates in the presence of topological changes in the solution that represents singular points in the evolution. For typical singularities the es...

In this paper, a priori error estimates are derived for the mixed finite element discretization of optimal control problems governed by fourth order elliptic partial differential equations. The state and co-state are discretized by RaviartThomas mixed finite element spaces and the control variable is approximated by piecewise constant functions. The error estimates derived for the state variabl...

This paper addresses the numerical approximation of Young measures appearing as generalized solutions to scalar nonconvex variational problems. We prove a priori and a posteriori error estimates for a macroscopic quantity, the stress. For a scalar three-well problem we show convergence of other quantities such as Young measure support and microstructure region. Numerical experiments indicate th...

In the study of pattern formation in bi–stable systems, the extended Fisher–Kolmogorov (EFK) equation plays an important role. In this paper, some a priori bounds are proved using Lyapunov functional. Further, existence, uniqueness and regularity results for the weak solutions are derived. Using C1-conforming finite element method, optimal error estimates are established for the semidiscrete ca...

The system of unsteady Darcy’s equations considered here models the time-dependent flow of an incompressible fluid such as water in a rigid porous medium. We propose a discretization of this problem that relies on a backward Euler’s scheme for the time variable and finite elements for the space variables. We prove a priori error estimates that justify the optimal convergence properties of the d...

Abstract This article considers a coupled finite and boundary element method for an interface problem the acoustic wave equation. Well-posedness, priori posteriori error estimates are discussed symmetric space-time Galerkin discretization related to energy. Numerical experiments in three dimensions illustrate performance of model problems.

We consider the regularity of an interface between two incompressible and inviscid fluids flows in the presence of surface tension. We obtain local in time estimates on the interface in H 3 2 k+1 and the velocity fields in H 3 2 . These estimates are obtained using geometric considerations which show that the Kelvin-Helmholtz instabilities are a consequence of a curvature calculation.

We consider a fractional order integro-differential equation with a weakly singular convolution kernel. The equation with homogeneuos Dirichlet boundary conditions is reformulated as an abstract Cauchy problem, and well-posedness is verified in the context of linear semigroup theory. Then we formulate a continuous Galerkin method for the problem, and we prove stability estimates. These are then...