SIAM Journal on Numerical Analysis

We establish a unified framework for $L^2$ error analysis for high order Lagrange finite volume methods on triangular meshes. Orthogonal conditions are originally proposed to construct dual partitions on triangular meshes, such that the corresponding finite ...

We consider robust iterative methods for discontinuous Galerkin (DG) $H(div,\Omega)$-conforming discretizations of the Brinkman equations. We describe a simple Uzawa iteration for the solution of this problem, which requires the solution of a nearly ...

Large time step (LTS) explicit schemes in the form originally proposed by LeVeque [Comm. Pure Appl. Math., 37 (1984), pp. 463--477] have seen a significant revival in recent years. In this paper we consider a general framework of local (2k+1)-point ...

Strong stability preserving (SSP) methods are designed primarily for time integration of nonlinear hyperbolic PDEs, for which the permissible SSP step size varies from one step to the next. We develop the first SSP linear multistep methods (of order two and ...

In this paper, we analyze the stability and error estimate of a decoupled method for a fluid-fluid interaction problem. This method applies the partitioned time stepping method to decouple the coupling system, which is the implicit/explicit scheme and was ...

In this work, the convergence analysis of explicit exponential time integrators based on general linear methods for quasi-linear parabolic initial boundary value problems is pursued. Compared to other types of exponential integrators encountering rather ...

This paper derives analytical estimates for the rates of convergence of numerical first and second derivative operators involved in flux reconstruction (FR). These estimates yield the rate of convergence for steady-state advection-diffusion problems when ...

We provide in the present paper a corrected proof for the classical quadratical convergence theorem (i.e., Theorem 3.3 in Friedland, Nocedal, and Overton [SIAM J. Numer. Anal., 24 (1987), pp. 634--667]) of the Newton-like method for solving inverse ...

We propose a new formulation along with a family of finite element schemes for the approximation of the interaction between fluid motion and linear mechanical response of a porous medium, known as Biot's consolidation problem. The steady-state version of ...

We consider numerical methods for initial value problems that employ a two-stage approach consisting of solution on a relatively coarse discretization followed by solution on a relatively fine discretization. Examples include adaptive error control, ...

We propose two adaptations of linear Hermite subdivision schemes to operate on manifold-valued data. Our approach is based on a Log-exp analogue and on projection, respectively, and can be applied to both interpolatory and noninterpolatory Hermite ...

We propose a mixed finite volume--finite element numerical method for solving the full Navier--Stokes--Fourier system describing the motion of a compressible, viscous, and heat conducting fluid. The physical domain occupied by the fluid has a smooth ...

This paper is devoted to a centered IMEX scheme in a multidimensional framework for a wide class of multicomponent and isentropic flows. The proposed strategy is based on a regularized model where the advection velocity is modified by the gradient of the ...

We consider the linear degenerate elliptic system of two first order equations ${\mathbf{u}}=-a(\phi)(\nabla{p} - \mathbf{g})$ and $\nabla\cdot(b(\phi)\mathbf{u})+\phi{p}=\phi^{1/2}{f}$, where $a$ and $b$ satisfy $a(0)=b(0)=0$ and are otherwise positive, and ...

The multiplicative Schwarz preconditioned inexact Newton (MSPIN) algorithm, based on decomposition by field type rather than by subdomain, was recently introduced to improve the convergence of systems with unbalanced nonlinearities. This paper provides a ...

In this paper we consider the full discretization of linear Maxwell's equations on spatial grids which are locally refined. For such problems, explicit time integration schemes become inefficient because the smallest mesh width results in a strict CFL ...