In this paper, we consider the div-curl problem posed on nonconvex polyhedral domains. We propose a least-squares method based on discontinuous elements with normal and tangential continuity across interior faces, as well as boundary conditions, weakly enforced through a properly designed least-squares functional. Discontinuous elements make it possible to take advantage of regularity of given ...

least squares method (lsm) is an accurate and rapid method for solving some analytical andnumerical problems. this method can be used to estimate the average reservoir pressure in well testanalysis. in fact, it may be employed to estimate parameters such as permeability (k) and porevolume (vp). regarding this point, buildup, drawdown, late transient test data, modified muskatmethod, interferenc...

A new meshless method for solving nonlinear boundary value problems, based on the local boundary integral equation (LBIE) method and the moving least squares approximation, is proposed in the present paper. The total formulation and a rate formulation are developed for the implementation of the present method. The present method does not need domain and boundary elements to deal with the volume...

The velocity-vorticity-pressure formulation of the steady-state incompressible Navier-Stokes equations in two dimensions is cast as a nonlinear least squares problem in which the functional is a weighted sum of squared residuals. A finite element discretization of the functional is minimized by a trust-region method in which the trust-region radius is defined by a Sobolev norm and the trust-reg...

We present a residual based artificial viscosity finite element method to solve conservation laws. The Galerkin approximation is stabilized by only residual based artificial viscosity, without any least-squares, SUPG, or streamline diffusion terms. We prove convergence of the method, applied to a scalar conservation law in two space dimensions, toward an unique entropy solution for implicit tim...

This paper looks to apply the mathematical framework of Theory Functional Connections solution boundary-value problems arising from hybrid systems. The is a technique derive constrained expressions which are analytical with embedded constraints. These particularly suitable transform large class optimization into unconstrained problems. initial and most useful application this in differential eq...

this paper investigates the connection between market valuation anda type of the merger (stock, cash) using real options setup. i solveexplicitly for the timing and terms of cash mergers in two deferent settingsto demonstrate that cash mergers generally occur at low marketvaluations, whereas stock mergers that may be observed at both low andhigh valuations; the result holds with some dierences...

A new sharp-interface immersed boundary method based approach for the computation of low-Mach number flow-induced sound around complex geometries is described. The underlying approach is based on a hydrodynamic/acoustic splitting technique where the incompressible flow is first computed using a second-order accurate immersed boundary solver. This is followed by the computation of sound using th...