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An interpolation-based method for solving Volterra integral equations
In this study, the second kind Volterra integral equations (VIEs) are considered. An algorithm based on the two-point Taylor formula as a special...
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Optimal control for cancer treatment mathematical model using Atangana–Baleanu–Caputo fractional derivative
In this work, optimal control for a fractional-order nonlinear mathematical model of cancer treatment is presented. The suggested model is determined...
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Discontinuous Galerkin via Interpolation: The Direct Flux Reconstruction Method
The discontinuous Galerkin (DG) method is based on the idea of projection using integration. The recent direct flux reconstruction (DFR) method by...
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Pointwise error estimates for linear finite element approximation to elliptic Dirichlet problems in smooth domains
In this paper, we consider pointwise error estimation for the linear finite element approximation to −Δ u + u = f in Ω, u = g on Γ, where Ω is a...
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Small errors imply large evaluation instabilities
Numerical analysts and scientists working in applications often observe that once they improve their techniques to get a better accuracy, some...
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Projection Based Semi-Implicit Partitioned Reduced Basis Method for Fluid-Structure Interaction Problems
In this manuscript a POD-Galerkin based Reduced Order Model for unsteady Fluid-Structure Interaction problems is presented. The model is based on a...
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The spectral implementation of the nonstationary Stokes problem with nonstandard boundary conditions
This paper deals with the implementation of the spectral discretization of the vorticity–velocity–pressure formulation of the nonstationary Stokes...
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Geometric Derivation and Analysis of Multi-Symplectic Numerical Schemes for Differential Equations
In the current work we present a class of numerical techniques for the solution of multi-symplectic PDEs arising at various physical problems. We...
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Crouzeix-Raviart finite element method for non-autonomous variational problems with Lavrentiev gap
We investigate the convergence of the Crouzeix-Raviart finite element method for variational problems with non-autonomous integrands that exhibit...
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Robust preconditioning techniques for multiharmonic finite element method with application to time-periodic parabolic optimal control problems
We are concerned with efficient solutions of the time-periodic parabolic optimal control problems. By using the multiharmonic FEM, the linear...
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Exponentially fitted methods with a local energy conservation law
A new exponentially fitted version of the discrete variational derivative method for the efficient solution of oscillatory complex Hamiltonian...
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Shape-Preservation Conditions for Cubic Spline Interpolation
We consider the problem on shape-preserving interpolation by classical cubic splines. Namely, we consider conditions guaranteeing that, for a...
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An a posteriori error estimate for a dual mixed method applied to Stokes system with non-null source terms
In this work, we focus our attention in the Stokes flow with nonhomogeneous source terms, formulated in dual mixed form. For the sake of...
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Geometric Derivation and Analysis of Multi-Symplectic Numerical Schemes for Differential Equations
In the current work we present a class of numerical techniques for the solution of multi-symplectic PDEs arising at various physical problems. We...
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Quadrature by fundamental solutions: kernel-independent layer potential evaluation for large collections of simple objects
Well-conditioned boundary integral methods for the solution of elliptic boundary value problems (BVPs) are powerful tools for static and dynamic...
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Divergence-Conforming Velocity and Vorticity Approximations for Incompressible Fluids Obtained with Minimal Facet Coupling
We introduce two new lowest order methods, a mixed method, and a hybrid discontinuous Galerkin method, for the approximation of incompressible flows....
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Approximation of Differential Operators with Boundary Conditions
AbstractThe use of spectral methods for solution of boundary value problems is very effective but involves great technical difficulties associated...
