For the (n + 2)-point Gauss–Jacobi–Lobatto quadrature to integrals with the Jacobi weight function ( 1 − t ) α ( 1 + t ) β (α > − 1, β > − 1) over the interval [ − 1 , 1 ], we estimate the location where the kernel of the error functional for ...

In this paper, we apply the weak Galerkin (WG) finite element method to solve the singularly perturbed fourth-order boundary value problem in a 2D domain. A Shishkin mesh is used to ensure that the method exhibits uniform convergence, regardless ...

A fast element-free Galerkin (EFG) method is proposed in this paper for solving the nonlinear complex Ginzburg–Landau equation. A second-order accurate time semi-discrete system is presented by using the Crank–Nicolson scheme for the temporal ...

We derive a discretization of the Caputo and Riemann–Liouville spatial derivatives by means of the meshless Generalized Finite Difference Method, which is based on moving least squares. The conditional convergence of the method is proved and ...

Due to its non-intrusive nature and ease of implementation, the Non-Intrusive Reduced Basis (NIRB) two-grid method has gained significant popularity in numerical computational fluid dynamics simulations. The efficiency of the NIRB method hinges ...

• A NIRB two-grid method is developed to introduce upscaled model parameters along with coarse grids.
• Numerical examples address flow and transport problems in heterogeneous porous media.

In this article, by combining high-order interpolation on coarse meshes and low-order finite element solutions on fine meshes, we propose a novel approach to improve the accuracy of the finite element method. The new method is in general suitable ...

In this work, we study, from the numerical point of view, a heat conduction model which is described by the history dependent version of the Moore–Gibson–Thompson equation. First, we consider the thermal problem, introducing a fully discrete ...

In this paper we present a novel mathematical model to describe the permeation of a fluid through a polymeric matrix, loaded with drug molecules, followed by its subsequent desorption. Both phenomena are enhanced by temperature. We deduce energy ...

In this paper, we present an implicit Crank–Nicolson finite element (FE) scheme for solving a nonlinear Schrödinger–type system, which includes Schrödinger–Helmholz system and Schrödinger–Poisson system. In our numerical scheme, we employ an ...

This work presents a domain decomposition method for the fluid-poroelastic structure interaction (FPSI) system, which utilizes local time integration for subproblems. To derive the domain decomposition scheme, we introduce a Lagrange multiplier ...

• We propose a domain decomposition method that enables the use of local time stepping.
• An interface problem is formulated based on the Steklov–Poincaré operator.
• The fluid and structure subproblems are solved independently using ...

Recently, the relaxation technique has been widely used to impose conservation of invariants while retaining the full accuracy of the original method. So far, only a single invariant of a system has been considered. In this work, by a mild ...

In the present paper, the new Kudryashov approach is utilized to construct several novel optical soliton solutions for the generalized integrable (2 + 1)-dimensional nonlinear Schrödinger system with conformable derivative. Additionally, the ...

The well-known high order stabilized codes (such as DUMKA and ROCK) have several drawbacks: numerically obtained stability polynomials (which do not have a closed analytic form), poor internal stability and convergence. RKC-type methods have much ...

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In this paper, we propose a numerical algorithm that combines the fading regularization method with the method of fundamental solutions (MFS) to solve a Cauchy problem associated with the biharmonic equation. We introduce a new stopping criterion ...

This paper constructs a linearized transformed L 1 virtual element method for the generalized nonlinear coupled time-fractional Schrödinger equations. The solutions to such problems typically exhibit singular behavior at the beginning. To avoid ...

The paper is devoted to the study of the backward behavior of solutions of the initial boundary value problem for the chevron pattern equations under homogeneous Dirichlet’s boundary conditions. We prove that, as t → ∞, the asymptotic behavior of ...

With the development of multi-layer elastic systems in the field of engineering mechanics, the corresponding variational inequality theory and algorithm design have received more attention and research. In this study, a class of equivalent saddle ...

Recently, researchers have investigated the relationship between proper orthogonal decomposition (POD), difference quotients (DQs), and pointwise in time error bounds for POD reduced order models of partial differential equations. In a recent ...

Interface problems, where distinct materials or physical domains meet, pose significant challenges in numerical simulations due to the discontinuities and sharp gradients across interfaces. Traditional finite element methods struggle to capture ...

In the past, the domain decomposition method was developed successfully for solving large-scale linear systems. However, the problems with significant nonlocal effect remain a major challenger for applying the method efficiently. In order to sort ...