In this note we investigate the question of higher regularity up to the boundary for quasilinear elliptic systems which origin from the time-discretization of models from infinitesimal elasto-plasticity. Our main focus lies on an elasto-plastic Cosserat model. More specifically we show that the time discretization renders H-regularity of the displacement and H-regularity for the symmetric plast...

    In this paper, a variational iteration method (VIM), which is a well-known method for solving nonlinear equations, has been employed to solve an inverse parabolic partial differential equation. Inverse problems in partial differential equations can be used to model many real problems in engineering and other physical sciences. The VIM is to construct correction functional using general Lagr...

For many elliptic PDE problems, finite-difference and finite-element methods are the techniques of choice. In a finite-difference approach, a solution uk on a set of discrete gridpoints 1, . . . , k is searched for. The discretized partial differential equation and boundary conditions create linear relationships between the different values of uk. In the finite-element method, the solution is e...

Many problems in applied mathematics, physics, and engineering require the solution of the heat equation in unbounded domains. Integral equation methods are particularly appropriate in this setting for several reasons: they are unconditionally stable, they are insensitive to the complexity of the geometry, and they do not require the artificial truncation of the computational domain as do finit...

The Lax-Richtmyer theorem is extended to work in the framework of Stetter's theory of discretizations. The new result applies to both initial and boundary value problems discretized by finite elements, finite differences, etc. Several examples are given, together with a comparison with other available equivalence theorems. The proof relies on a generalized Banach-Steinhaus theorem.

We present a second-order accurate projection method to solve the incompressible Navier-Stokes equations on irregular domains in two and three dimensions. We use a finite-volume discretization obtained from intersecting the irregular domain boundary with a Cartesian grid. We address the small-cell stability problem associated with such methods by hybridizing a conservative discretization of the...

Successful employment of numerical techniques for the forward and inverse electrocardiographic (ECG) problems requires the ability to both quantify and minimize approximation errors introduced as part of the discretization process. Conventional finite element discretization and refinement strategies effective for the forward problem may become inappropriate for the inverse problem because of it...

A continuous adjoint method for Aerodynamic Shape Optimization (ASO) using the compressible Reynolds-Averaged Navier-Stokes (RANS) equations and the Baldwin-Lomax turbulence model was implemented and tested. The resulting implementation was used to determine the accuracy in the calculation of aerodynamic gradient information for use in ASO problems. For completeness, the formulation and discret...

When one solves differential equations, modeling biological or physical phenomena, it is of great importance to take physical constraints into account. More precisely, numerical schemes have to be designed such that discrete solutions satisfy the same constraints as exact solutions. In this work, we introduce explicit finite difference schemes based on the nonstandard discretization method to a...

This paper deals with the numerical approximation of the solution of 1D parabolic singularly perturbed problems of reaction–diffusion type. The numerical method combines the standard implicit Euler method on a uniform mesh to discretize in time and a HODIE compact fourth order finite difference scheme to discretize in space, which is defined on a priori special meshes condensing the grid points...