We analyze the spatially semidiscrete piecewise linear finite element method for a nonlocal parabolic equation resulting from thermistor problem. Our approach is based on the properties of the elliptic projection defined by the bilinear form associated with the variational formulation of the finite element method. We assume minimal regularity of the exact solution that yields optimal order erro...

Abstract. Dense, non-aqueous phase liquids (DNAPLs) are common organic contaminants in subsurface environment. Once spilled or leaked underground, they slowly dissolved into groundwater and generated a plume of contaminants. In order to manage the contaminated site and predict the behavior of dissolved DNAPL in heterogeneous subsurface requires a comprehensive numerical model. In this work, the...

We study a generalized Crank–Nicolson scheme for the time discretization of a fractional wave equation, in combination with a space discretization by linear finite elements. The schemeuses a non-uniformgrid in time to compensate for the singular behaviour of the exact solution at t = 0. With appropriate assumptions on the data and assuming that the spatial domain is convex or smooth, we show th...

For the Schrödinger-Poisson system, we propose an ALmost EXact(ALEX) boundary condition to treat accurately the numerical boundaries. Being local in both space and time, the ALEX boundary conditions are demonstrated to be effective in suppressing spurious numerical reflections. Together with the Crank-Nicolson scheme, we simulate a resonant tunneling diode. The algorithm produces numerical resu...

A steady-state and transient finite element model has been developed to approximate, with simple triangular elements, the two-dimensional advection—diffusion equation for practical river surface flow simulations. Essentially, the space—time Crank—Nicolson—Galerkin formulation scheme was used to solve for a given conservative flow-field. Several kinds of point sources and boundary conditions, na...

We show that the Strang splitting method applied to a diffusion-reaction equation with inhomogeneous general oblique boundary conditions is of order two when diffusion solved Crank-Nicolson method, while reduction occurs in if using other Runge-Kutta schemes or even exact flow itself for part. prove these results source term only depends on space variable, an assumption which makes scheme equiv...

In this paper, a Crank–Nicolson finite difference scheme based on cubic B-spline quasi-interpolation has been derived for the solution of coupled Burgers equations with Caputo–Fabrizio derivative. The first- and second-order spatial derivatives have approximated by first second quasi-interpolation. discrete obtained in way constitutes system algebraic associated bi-pentadiagonal matrix. We show...