SIAM Journal on Numerical Analysis

In highly diffusive regimes, the transfer equation with anisotropic boundary conditions has an asymptotic behavior as the mean free path $\epsilon$ tends to zero that is governed by a diffusion equation and boundary conditions obtained through a matched ...

We present a new Lagrange multiplier-based domain decomposition method for solving iteratively systems of equations arising from the finite element discretization of plate bending problems. The proposed method is essentially an extension of the finite ...

This paper introduces a new class of methods, which we call Möbius schemes, for the numerical solution of matrix Riccati differential equations. The approach is based on viewing the Riccati equation in its natural geometric setting, as a flow on the ...

We formulate an alternating direction implicit Crank--Nicolson scheme for solving a general linear variable coefficient parabolic problem in nondivergence form on a rectangle with the solution subject to nonhomogeneous Dirichlet boundary condition. ...

This paper is devoted to the spectral element discretization of the Laplace equation in a disk when provided with discontinuous boundary data. Relying on an appropriate variational formulation, we propose a discrete problem and prove its convergence. ...

The first boundary value problem for a nonlinear Schrödinger equation is investigated. The conditional convergence and stability on the initial data of the explicit three-level difference scheme of DuFort--Frankel type in C and W_2^1$ norms are proved. ...

For three-dimensional simulations of the vortex phenomena in superconductors based on the Ginzburg--Landau (GL) theory, the physical variables must be solved in the whole space in general. Exact boundary conditions on an artificial boundary are ...

A numerical scheme for the nonstationary Boltzmann equation in the incompressible Navier--Stokes limit is developed. The scheme is induced by the asymptotic analysis of the Navier--Stokes limit for the Boltzmann equation. It works uniformly for all ...

The subject of this paper is the analysis of error estimates of the combined finite volume--finite element (FV--FE) method for the numerical solution of a scalar nonlinear conservation law equation with a diffusion term. Nonlinear convective terms are ...

Backward error analysis has become an important tool for understanding the long time behavior of numerical integration methods. This is true in particular for the integration of Hamiltonian systems where backward error analysis can be used to show that ...

We prove that, up to higher order perturbation terms, edge residuals yield global upper and local lower bounds on the error of linear finite element methods both in H¹- and L²-norms. We present two proofs: one uses the standard L²-projection and the ...

In this paper, we consider several high-order schemes in one space dimension. In particular, we compare the second-order relaxation ($\epsilon<<1$) or "relaxed" ($\epsilon=0$) schemes of Jin and Xin [ Comm. Pure Appl. Math. , 48 (1995), pp. 235--277] ...

Using the theory of n-widths, the approximability of solutions of singularly perturbed linear reaction-diffusion problems in two dimensions is quantified.

We describe an algorithm for the numerical computation of the rank-one convex envelope of a function $f:\MM^{m\times n}\rightarrow\RR$. We prove its convergence and an error estimate in $L^\infty$.

Hierarchical a posteriori error estimators are introduced and analyzed for mortar finite element methods. A weak continuity condition at the interfaces is enforced by means of Lagrange multipliers. The two proposed error estimators are based on a ...