相关论文: About optimization of methods for mixed derivative…
The problem of optimal recovering high-order mixed derivatives of bivariate functions with finite smoothness is studied. Based on the truncation method, an algorithm for numerical differentiation is constructed, which is order-optimal both…
The problem of recovering partial derivatives of high orders of bivariate functions with finite smoothness is studied. Based on the truncation method, a numerical differentiation algorithm was constructed, which is optimal by the order,…
In this paper, we study optimization problems of numerical differentiation and summation methods on classes of univariate functions. Sharp estimates (in order) of the optimal recovery error and information complexity are calculated for…
The problems of optimal recovery of unbounded operators are studied. Optimality means the highest possible accuracy and the minimal amount of discrete information involved. It is established that the truncation method, when certain…
The work provides an upper estimate of the best accuracy for the problem of reconstructing derivatives based on function values at a given number of points for the functions of Besov classes meeting the mixed Hoelder conditions. In some…
Scientific studies often require the precise calculation of derivatives. In many cases an analytical calculation is not feasible and one resorts to evaluating derivatives numerically. These are error-prone, especially for higher-order…
A hybridized discontinuous Galerkin method is proposed for solving 2D fractional convection-diffusion equations containing derivatives of fractional order in space on a finite domain. The Riemann-Liouville derivative is used for the spatial…
We study the problem of numerical differentiation of functions from weighted Wiener classes. We construct and analyze a truncation Legendre method to recover arbitrary order derivatives. The main focus is on obtaining error estimates in…
In this paper, we are concerned with a nonlinear optimal control problem of ordinary differential equations. We consider a discretization of the problem with the discontinuous Galerkin method with arbitrary order $r \in \mathbb{N}\cup…
We develop a hybrid spatial discretization for the wave equation in second order form, based on high-order accurate finite difference methods and discontinuous Galerkin methods. The hybridization combines computational efficiency of finite…
We present a novel approach for high-order accurate numerical differentiation on unstructured meshes of quadrilateral elements. To differentiate a given function, an auxiliary function with greater smoothness properties is defined which…
This paper presents a hybridized formulation for the weak Galerkin finite element method for the biharmonic equation. The hybridized weak Galerkin scheme is based on the use of a Lagrange multiplier defined on the element boundaries. The…
A conforming discontinuous Galerkin finite element method is introduced for solving the biharmonic equation. This method, by its name, uses discontinuous approximations and keeps simple formulation of the conforming finite element method at…
A novel mixed spectral-Galerkin method based on generalized ball polynomials is proposed for solving the biharmonic equation on a unit ball. By introducing an auxiliary variable to decouple the biharmonic equation into a system of…
We discuss the mathematical modeling and numerical discretization of transport problems on one-dimensional networks. Suitable coupling conditions are derived that guarantee conservation of mass across network junctions and dissipation of a…
The optimal value function is one of the basic objects in the field of mathematical optimization, as it allows the evaluation of the variations in the cost/revenue generated while minimizing/maximizing a given function under some…
This paper, as the sequel to previous work, develops numerical schemes for fractional diffusion equations on a two-dimensional finite domain with triangular meshes. We adopt the nodal discontinuous Galerkin methods for the full spatial…
In this study, we examine numerical approximations for 2nd-order linear-nonlinear differential equations with diverse boundary conditions, followed by the residual corrections of the first approximations. We first obtain numerical results…
In the framework of ODEs, we uncover a new link between the continuous Galerkin method (see Math. Comp. (1972), 26 (118 and 120), 415-426 and 881-891) and the discontinuous Galerkin method (see Mathematical Aspects of Finite elements in…
A new weak Galerkin (WG) finite element method for solving the biharmonic equation in two or three dimensional spaces by using polynomials of reduced order is introduced and analyzed. The WG method is on the use of weak functions and their…