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Optimal A Priori Error Estimates for Elliptic Interface Problems: Weak Galerkin Mixed Finite Element Approximations
We consider weak Galerkin mixed finite element approximations of second order elliptic equations on domains that can be described as a union of...
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A Priori Error Bounds for Parabolic Interface Problems with Measure Data
AbstractThis article studies a priori error analysis for linear parabolic interface problems with measure data in time in a bounded convex polygonal...
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A Priori and a Posteriori Error Analysis of TDNNS Method for Linear Elasticity Problem Under Minimal Regularity
In this paper, a priori and a posteriori error estimates of the tangential-displacement normal-normal-stress (TDNNS) method for linear elasticity...
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The a Priori and a Posteriori Error Estimates of DG Method for the Steklov Eigenvalue Problem in Inverse Scattering
In this paper, we study the discontinuous Galerkin finite element method for the Steklov eigenvalue problem arising in inverse scattering. We present...
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Error Estimates of hp Spectral Element Methods in Nonlinear Optimal Control Problem
The main purpose of this paper is to discuss hp spectral element method for optimal control problem governed by a nonlinear elliptic equation with
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A Priori Error Estimate of Deep Mixed Residual Method for Elliptic PDEs
In this work, we derive a priori error estimate of the deep mixed residual method (DMRM) when solving some elliptic partial differential equations...
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Higher-order error estimates for physics-informed neural networks approximating the primitive equations
Large-scale dynamics of the oceans and the atmosphere are governed by primitive equations (PEs). Due to the nonlinearity and nonlocality, the...
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A posteriori error estimates for wave maps into spheres
We provide a posteriori error estimates in the energy norm for temporal semi-discretisations of wave maps into spheres that are based on the angular...
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Error estimates for mixed and hybrid FEM for elliptic optimal control problems with penalizations
Mixed and hybrid finite element discretizations for distributed optimal control problems governed by an elliptic equation are analyzed. A cost...
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Error Estimates for Fractional Semilinear Optimal Control on Lipschitz Polytopes
We adopt the integral definition of the fractional Laplace operator and analyze solution techniques for fractional, semilinear, and elliptic optimal...
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Optimal error estimates of an IPDG scheme for the resistive magnetic induction equation
In this paper, we develop the framework for error analysis of a fully-discrete interior penalty discontinuous Galerkin (IPDG) scheme designed for the...
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A New A Posteriori Error Estimates for Optimal Control Problems Governed by Parabolic Integro-Differential Equations
AbstractIn this paper, we provide a new a posteriori error analysis for linear finite element approximation of a parabolic integro-differential...
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Pointwise Error Estimates of Numerical Solutions to Linear Quadratic Optimal Control Problems
An auxiliary optimal control problem is formulated that provides with its unique solution, a continuous representation of the global error of a...
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A priori error estimates of discontinuous Galerkin methods for a quasi-variational inequality
We study a priori error estimates of discontinuous Galerkin (DG) methods for solving a quasi-variational inequality, which models a frictional...
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Ritz-type projectors with boundary interpolation properties and explicit spline error estimates
In this paper we construct Ritz-type projectors with boundary interpolation properties in finite dimensional subspaces of the usual Sobolev space and...
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Error Estimates of Finite Element Method for the Incompressible Ferrohydrodynamics Equations
In this paper, we consider the Shliomis ferrofluid model and study its numerical approximation. We investigate a first-order energy-stable fully...
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Error Estimates of EDG-HDG Methods for the Stokes Equations with Dirac Measures
In this paper, we analyze the hybridized, embedded-hybridized and embedded discontinuous Galerkin methods for the Stokes equations with Dirac...
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A posteriori error estimates for a dual finite element method for singularly perturbed reaction–diffusion problems
A posteriori error estimates are established for a two-step dual finite element method for singularly perturbed reaction–diffusion problems. The...
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A posteriori error estimates of a DG method for optimal control problems governed by the transport equation
In the paper, we derive a posteriori error estimates of a discontinuous Galerkin (DG) finite element method for optimal control problems governed by...
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Optimal error estimates of spectral Galerkin method for mixed diffusion equations
We present a highly accurate and efficient spectral Galerkin method for the advection–diffusion–reaction equations with fractional lower-order terms...