We consider unsteady poroelasticity problem in fractured porous medium within the classical Barenblatt double-porosity model. For numerical solution of doubleporosity poroelasticity problems we construct splitting schemes with respect to physical processes, where transition to a new time level is associated with solving separate problem for the displacements and fluid pressures in pores and fra...

In this letter, we present a computational framework based on the use of the Newton and level set methods and tailored for the modeling of bubbles with surface tension in a surrounding Newtonian fluid. We describe a fully implicit and monolithic finite element method that maintains stability for significantly larger time steps compared to the usual explicit method and features substantial compu...

The Galerkin method is applied to a pair of functions. It is demonstrated that this system can be linear and then nonlinear primitive (wave) equations. efficiently solved by an implicit method. Numerical This results in a system of ordinary differential equations. examples show that integration using the Galerkin method Procedures are included for generating the coefficient is more efficient th...

We present and analyze an implicit–explicit timestepping procedure with finite element spatial approximation for semilinear reaction–diffusion systems on evolving domains arising from biological models, such as Schnakenberg’s (1979). We employ a Lagrangian formulation of the model equations which permits the error analysis for parabolic equations on a fixed domain but introduces technical diffi...

We discuss Q-balls in the complex signum-Gordon model in d-dimensional space for d = 1, 2, 3. The Q-balls have strictly finite size. Their total energy is a power-like function of the conserved U (1) charge with the exponent equal to (d + 2)(d + 3) −1. In the cases d = 1 and d = 3 explicit analytic solutions are presented.

Osmosis filters are based on drift–diffusion processes. They offer nontrivial steady states with a number of interesting applications. In this paper we present a fully discrete theory for linear osmosis filtering that follows the structure of Weickert’s discrete framework for diffusion filters. It regards the positive initial image as a vector and expresses its evolution in terms of iterative m...

Variable-order fractional diffusion equation model is a recently developed and promising approach to characterize time-dependent or concentration-dependent anomalous diffusion, or diffusion process in inhomogeneous porous media. To further study the properties of variableorder time fractional subdiffusion equation models, the efficient numerical schemes are urgently needed. This paper investiga...

A new analytic approach to investigate the zero-temperature time evolution of Jaynes-Cummings system with cavity losses is developed. With realistic coupling between and environment assumed, a simple master equation derived, leading explicit solution for resonant case. This suitable analyses not only on single excitation states but also many states, which enables us photon coherent state observ...

We study fully discrete linearized Galerkin finite element approximations to a nonlinear gradient flow, applications of which can be found in many areas. Due to the strong nonlinearity of the equation, existing analyses for implicit schemes require certain restrictions on the time step and no analysis has been explored for linearized schemes. This paper focuses on the unconditionally optimal L2...

We approximate the solution of initial boundary value problems for nonlinear parabolic equations. In space we discretize by finite element methods. The discretization in time is based on linear multistep schemes. One part of the equation is discretized implicitly and the other explicitly. The resulting schemes are stable, consistent and very efficient, since their implementation requires at eac...