Journal of Scientific Computing

This work is motivated by the investigation of a fractional extension of a general nonlinear multidimensional wave equation with damping. The model under study considers partial derivatives of orders in $$(0, 1) \cup (1, 2]$$(0,1)?(1,2] with respect to ...

In this paper, the two-dimensional multi-term time-space fractional diffusion-wave equation on an irregular convex domain is considered as a much more general case for wider applications in fluid mechanics. A novel unstructured mesh finite element ...

In this article, we address the numerical solution of the Dirichlet problem for the three-dimensional elliptic Monge---Ampère equation using a least-squares/relaxation approach. The relaxation algorithm allows the decoupling of the differential ...

We present an efficient algorithm for recent generalizations of optimal mass transport theory to matrix-valued and vector-valued densities. These generalizations lead to several applications including diffusion tensor imaging, color image processing, ...

Due to the indefiniteness and poor spectral properties, the discretized linear algebraic system of the vector Laplacian by mixed finite element methods is hard to solve. A block diagonal preconditioner has been developed and shown to be an effective ...

The computation of the Mittag-Leffler (ML) function with matrix arguments, and some applications in fractional calculus, are discussed. In general the evaluation of a scalar function in matrix arguments may require the computation of derivatives of ...

In this work we prove that the original (Bassi and Rebay in J Comput Phys 131:267---279, 1997) scheme (BR1) for the discretization of second order viscous terms within the discontinuous Galerkin collocation spectral element method (DGSEM) with Gauss ...

An open-source code that implements the entropy stable discontinuous Galerkin scheme with Legendere---Gauss---Lobatto collocation (DGSEM) on curved unstructured hexahedral grids for compressible Navier---Stokes equations (NSE) is available at github.com/...

We consider an identification (inverse) problem, where the state $${\mathsf {u}}$$u is governed by a fractional elliptic equation and the unknown variable corresponds to the order $$s \in (0,1)$$sý(0,1) of the underlying operator. We study the existence ...

We propose and study a class of numerical schemes to approximate time-fractional differential equations. The methods are based on the approximations of the Caputo fractional derivative of order $$\alpha \in (0, 1)$$??(0,1) by using continuous piecewise ...

In this paper, we propose a high order characteristics tracing scheme for the two-dimensional nonlinear incompressible Euler system in vorticity stream function formulation and the guiding center Vlasov model. Such a scheme is incorporated into a semi-...

A unified fast time-stepping method for both fractional integral and derivative operators is proposed. The fractional operator is decomposed into a local part with memory length $$\varDelta T$$ΔT and a history part, where the local part is approximated ...

The purpose of this work is to study a finite element method for finding solutions to the eigenvalue problem for the fractional Laplacian. We prove that the discrete eigenvalue problem converges to the continuous one and we show the order of such ...

In this paper, we consider electromagnetic (EM) wave propagation in nonlinear optical media in one spatial dimension. We model the EM wave propagation by the time-dependent Maxwell's equations coupled with a system of nonlinear ordinary differential ...

We analyse the dispersion properties of two types of explicit finite element methods for modelling acoustic and elastic wave propagation on tetrahedral meshes, namely mass-lumped finite element methods and symmetric interior penalty discontinuous ...

We present a new iterative technique based on radial basis function (RBF) interpolation and smoothing for the generation and smoothing of curvilinear meshes from straight-sided or other curvilinear meshes. Our technique approximates the coordinate ...

We present an efficient numerical algorithm to solve random interface grating problems based on a combination of shape derivatives, the weak Galerkin method, and a low-rank approximation technique. By using the asymptotic perturbation approach via shape ...

We derive a posteriori error estimates for the hybridizable discontinuous Galerkin (HDG) methods, including both the primal and mixed formulations, for the approximation of a linear second-order elliptic problem on conforming simplicial meshes in two ...

A novel discontinuous Galerkin (DG) method is developed to solve time-dependent bi-harmonic type equations involving fourth derivatives in one and multiple space dimensions. We present the spatial DG discretization based on a mixed formulation and ...

A hybrid staggered discontinuous Galerkin method is developed for the Korteweg---de Vries equation. The equation is written into a system of first order equations by introducing auxiliary variables. Two sets of finite element functions are introduced to ...

In this paper, we deal with an optimal control problem governed by the convection diffusion equations with random field in its coefficients. Mathematically, we prove the necessary and sufficient optimality conditions for the optimal control problem. ...

A new hybrid optimized low-dissipation and adaptive MUSCL scheme is present for finite volume method. The proposed scheme, based on an optimized linear scheme with monotonicity preserving limitation and an adaptive MUSCL scheme, emphasizes on the ...

A smoothness-increasing accuracy conserving filtering approach to the regularization of discontinuities is presented for single domain spectral collocation approximations of hyperbolic conservation laws. The filter is based on convolution of a ...

The study of surface mappings or deformations plays an important role for various applications in computer visions and graphics. An accurate and effective method to measure and control geometric distortions of the mapping is therefore necessary. ...

A new linear implicit finite difference method is proposed for the approximation of the solution to a periodic, initial value problem for a Schrödinger---Hirota equation. Optimal, second order convergence in the discrete $$H^1$$H1-norm is proved, ...

We propose and analyze some efficient spectral/spectral element methods to solve singular eigenvalue problems related to the Schrödinger operator with an inverse-power potential. For the Schrödinger eigenvalue problem $$-\Delta u +V(x)u=\lambda u$$-Δu+V(...