Motivated by the partial differential equations of mixed type that arise in the reduction of the Einstein equations by a helical Killing vector field, we consider a boundary value problem for the helically-reduced wave equation with an arbitrary source in 2+1 dimensional Minkowski spacetime. The reduced equation is a second-order partial differential equation which is elliptic inside a disk and...

The sensitivity of a stratocumulus-capped mixed layer to a change in cloud droplet concentration is evaluated with a large-eddy simulation (LES) and a mixed layer model (MLM). The strength of the second aerosol indirect effect simulated by the two model types agrees within 50% for cases in which the LES-simulated boundary layer remains well mixed, if the MLM entrainment closure includes the eff...

We consider an initial boundary value problem for a symmetrizable mixed hyperbolic-parabolic system of conservation laws with a small viscosity ε, ut +F (u )x = ε(B(u)ux)x. When the boundary is noncharacteristic for both the viscous and the inviscid system, and the boundary condition dissipative, we show that uε converges to a solution of the inviscid system before the formation of shocks if th...

We study the condition number of the system matrices that appear in the Boundary Element Method when solving the Stokes equations at a two-dimensional domain. At the boundary of the domain we impose Dirichlet conditions or mixed conditions. We show that for certain critical boundary contours the underlying boundary integral equation is not solvable. As a consequence, the condition number of the...

We extend the applicability of the augmented dual-mixed method introduced recently in [4, 5] to the problem of linear elasticity with mixed boundary conditions. The method is based on the Hellinger–Reissner principle and the symmetry of the stress tensor is imposed in a weak sense. The Neuman boundary condition is prescribed in the finite element space. Then, suitable Galerkin least-squares typ...

This work is concerned with the discontinuous Galerkin finite approximations for the steady Stokes equations driven by slip boundary condition of “friction” type. Assuming that the flow region is a bounded, convex domain with a regular boundary, we formulate the problem and its discontinuous Galerkin approximations as mixed variational inequalities of the second kind with primitive variables. T...

We consider the augmented mixed finite element method introduced in [7] for the equations of plane linear elasticity with mixed boundary conditions. We develop an a posteriori error analysis based on the Ritz projection of the error and obtain an a posteriori error estimator that is reliable and efficient, but that involves a non-local term. Then, introducing an auxiliary function, we derive fu...

in this work, we introduce the unsteady incompressible Navier-Stokes equations with a new boundary condition, generalizes the Dirichlet and the Neumann conditions. Then we derive an adequate variational formulation of timedependent NavierStokes equations. We then prove the existence theorem and a uniqueness result. A Mixed finite-element discretization is used to generate the nonlinear system c...