SIAM Journal on Numerical Analysis

We consider the construction of Markov chain approximations for an important class of deterministic control problems. The emphasis is on the construction of schemes that can be easily implemented and which possess a number of highly desirable ...

We propose a finite element method for approximating the nonlinear equations describing the electromagnetic field in a ferromagnetic material. Using energy arguments, we prove an optimal convergence rate for the method assuming a sufficiently smooth ...

We present a fast and accurate numerical scheme for the approximation of the primitive equations of the atmosphere. The temporal variable is discretized by using a special semi-implicit scheme which requires only to solve a Helmholtz equation and a ...

The nonoscillatory central difference scheme of Nessyahu and Tadmor is a Godunov-type scheme for one-dimensional hyperbolic conservation laws in which the resolution of Riemann problems at the cell interfaces is bypassed thanks to the use of the ...

A superconvergence result is established in this article for approximate solutions of second-order elliptic equations by mixed finite element methods over quadrilaterals. The superconvergence indicates an accuracy of ${\cal O}(h^{k+2})$ for the mixed ...

Accurate discrete analogs of differential operators that satisfy the identities and theorems of vector and tensor calculus provide reliable finite difference methods for approximating the solutions to a wide class of partial differential equations. ...

Composite overlapping grid methods were studied by Volkov [ Proceedings of the Steklov Institute of Mathematics, 96 (1968), pp. 145--185] and Starius [ Numer. Math., 28 (1977), pp. 243--258] more than 20 years ago. More recently several authors have ...

Lower-order errors downstream of a shock layer have been detected in computations with nonconstant solutions when using higher-order shock capturing schemes in one and two dimensions [B. Engquist and B. Sjögreen, {SIAM J. Numer. Anal., 35 (1998), pp. ...

Optimal Krylov subspace methods like GMRES and GCR have to compute an orthogonal basis for the entire Krylov subspace to compute the minimal residual approximation to the solution. Therefore, when the number of iterations becomes large, the amount of ...

The standard five-point difference approximation to the Cauchy problem for Laplace's equation satisfies stability estimates---and hence turns out to be a well-posed problem---when a certain boundedness requirement is fulfilled. The estimates are of ...

The numerical solution of wave scattering from large objects or from a large cluster of scatterers requires excessive computational resources and it becomes necessary to use approximate---but fast---methods such as the fast multipole method; however, ...

Symm's equation is a first-kind integral equation for computing conformal maps of simply connected regions. The package CONFPACK solves Symm's equation by an indirect boundary element method using an accurate corner representation. This solution ...

A family of explicit space-time finite element methods for the initial boundary value problem for linear, symmetric hyperbolic systems of equations is described and analyzed. The method generalizes the discontinuous Galerkin method and, as is typical ...

Conservatives and entropy schemes for the Fokker--Planck--Landau (FPL) equation are studied. We prove the existence of a unique positive and global in time solution for the homogeneous linear and nonlinear discretized (either in the velocity space or ...

We examine the effect of adaptively generated refined meshes on the P¹ - P¹ finite element method with semi-explicit time stepping of part I, which applies to a phase relaxation model with small parameter $\ep>0$. A typical mesh is highly graded in the ...