Search results for "Computation"

On Weakly Singular Integral Equations of the Second Kind

1988

A boundary min-max principle as a tool for boundary element formulations

1991

Abstract A min-max principle for elastic solids, expressed in terms of the unknown boundary displacements and tractions, is presented. It is shown that its Euler-Lagrange equations coincide with the classical boundary integral equations for displacements and for tractions. This principle constitutes a suitable starting point for a symmetric sign-definite formulation of the boundary element method.

On a new proof of Moser's twist mapping theorem

1976

Based on a new idea of the author, a new proof of J. Moser's twist mapping theorem is presented.

Monotonicity-based inversion of the fractional Schr\"odinger equation II. General potentials and stability

2019

In this work, we use monotonicity-based methods for the fractional Schr\"odinger equation with general potentials $q\in L^\infty(\Omega)$ in a Lipschitz bounded open set $\Omega\subset \mathbb R^n$ in any dimension $n\in \mathbb N$. We demonstrate that if-and-only-if monotonicity relations between potentials and the Dirichlet-to-Neumann map hold up to a finite dimensional subspace. Based on these if-and-only-if monotonicity relations, we derive a constructive global uniqueness results for the fractional Calder\'on problem and its linearized version. We also derive a reconstruction method for unknown obstacles in a given domain that only requires the background solution of the fractional Sch…

On a global superconvergence of the gradient of linear triangular elements

1987

Abstract We study a simple superconvergent scheme which recovers the gradient when solving a second-order elliptic problem in the plane by the usual linear elements. The recovered gradient globally approximates the true gradient even by one order of accuracy higher in the L 2 -norm than the piecewise constant gradient of the Ritz—Galerkin solution. A superconvergent approximation to the boundary flux is presented as well.

Existence and Singularities for the Prandtl Boundary Layer Equations

2000

Prandtl's boundary layer equations, first formulated in 1904, resolve the differences between the viscous and inviscid description of fluid flows. This paper presents a review of mathematical results, both analytic and computational, on the unsteady boundary layer equations. This includes a review of the derivation and basic properties of the equations, singularity formation, well-posedness results, and infinite Reynolds number limits.

Figures of equilibrium in close binary systems

1992

The equilibrium configurations of close binary systems are analyzed. The autogravitational, centrifugal and tidal potentials are expanded in Clairaut's coordinates. From the set of the total potential angular terms an integral equations system is derived. The reduction of them to ordinary differential equations and the determination of the boundary conditions allow a formulation of the problem in terms of a single variable.

Internal fe approximation of spaces of divergence-free functions in three-dimensional domains

1986

SUMMARY The space of divergence-free vector functions with vanishing normal flux on the boundary is approximated by subspaces of finite elements having the same property. An easy way of generating basis functions in these subspaces is shown.

Energy dissipative characteristic schemes for the diffusive Oldroyd-B viscoelastic fluid

2015

Domain decomposition in the symmetric boundary element analysis

2002

Recent developments in the symmetric boundary element method (SBEM) have shown a clear superiority of this formulation over the collocation method. Its competitiveness has been tested in comparison to the finite element method (FEM) and is manifested in several engineering problems in which internal boundaries are present, i.e. those in which the body shows a jump in the physical characteristics of the material and in which an appropriate study of the response must be used. When we work in the ambit of the SBE formulation, the body is subdivided into macroelements characterized by some relations which link the interface boundary unknowns to the external actions. These relations, valid for e…