Related papers: Galerkin Finite Element Method for Nonlinear Fract…
In this paper the numerical solution of non-autonomous semilinear stochastic evolution equations driven by an additive Wiener noise is investigated. We introduce a novel fully discrete numerical approximation that combines a standard…
We study a second order hyperbolic initial-boundary value partial differential equation with memory, that results in an integro-differential equation with a convolution kernel. The kernel is assumed to be either smooth or no worse than…
We provide the convergence analysis for a sinc-Galerkin method to solve the fractional Dirichlet problem. This can be understood as a follow-up of an earlier article by the same authors, where the authors presented a sinc-function based…
This paper is concerned with finite element approximations of $W^{2,p}$ strong solutions of second-order linear elliptic partial differential equations (PDEs) in non-divergence form with continuous coefficients. A nonstandard (primal)…
In this paper, we consider a class of nonlinear fractional differential equations involving Hilfer derivative with boundary conditions. First, we obtain an equivalent integral for the given boundary value problem in weighted space of…
We propose and analyze a space-time finite element method for Westervelt's quasilinear model of ultrasound waves in second-order formulation. The method combines conforming finite element spatial discretizations with a…
The numerical solution of strain gradient-dependent continuum problems has been dogged by continuity demands on the basis functions. For most commonly accepted models, solutions using the finite element method demand $C^{1}$ continuity of…
In this paper we study the numerical method for approximating the random periodic solution of semiliear stochastic evolution equations. The main challenge lies in proving a convergence over an infinite time horizon while simulating…
We use a finite element approach based on Galerkin method to obtain approximate steady state solutions of the thermistor problem with temperature dependent electrical conductivity.
We develop a fully discrete scheme for time-fractional diffusion equations by using a finite difference method in time and a finite element method in space. The fractional derivatives are used in Caputo sense. Stability and error estimates…
In this study, a Galerkin finite element method is presented for time-fractional stochastic heat equation driven by multiplicative noise, which arises from the consideration of heat transport in porous media with thermal memory with random…
When solving the Poisson equation by the finite element method, we use one degree of freedom for interpolation by the given Laplacian - the right hand side function in the partial differential equation. The finite element solution is the…
We prove existence of weak solutions to the Cauchy problem corresponding to various strictly parabolic equations on a compact Riemannian manifold $(M,g)$. This also includes strictly parabolic equations with stochastic forcing with linear…
This paper introduces a new variational formulation for Dirichlet boundary control problem of elliptic partial differential equations, based on observations that the state and adjoint state are related through the control on the boundary of…
A finite element approach to solve numerically the Takagi-Taupin equations expressed in a weak form is presented and applied to simulate X-ray reflectivity curves, spatial intensity distributions and focusing properties of bent perfect…
This work proposes a nonlinear finite element method whose nodal values preserve bounds known for the exact solution. The discrete problem involves a nonlinear projection operator mapping arbitrary nodal values into bound-preserving ones…
We couple the L1 discretization for Caputo derivative in time with spectral Galerkin method in space to devise a scheme that solves quasilinear subdiffusion equations. Both the diffusivity and the source are allowed to be nonlinear…
We propose a nodal discontinuous Galerkin method for solving the nonlinear Riesz space fractional Schr\"{o}dinger equation and the strongly coupled nonlinear Riesz space fractional Schr\"{o}dinger equations. These problems have been…
This paper is concerned with the approximation of solutions to a class of second order non linear abstract differential equations. The finite-dimensional approximate solutions of the given system are built with the aid of the projection…
We study the Dirichlet boundary-value problem of steady-state two-sided variable-coefficient conservative space-fractional diffusion equations. We show that the Galerkin weak formulation, which was proved to be coercive and continuous for a…