Convergence and a Priori Error Estimates
Error Estimations, Error Computations, and Convergence Rates in FEM for BVPs
... a priori estimates only hold in asymptotic range and their derivation in the currently published literature are only valid for self adjoint operators in GM/WF when functional B ( ) ⋅ ⋅ , is symmetric, thus ...
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A priori error estimates for optimal control problems with pointwise constraints on the gradient of the state
... Abstract. We analyze a finite element approximation of an elliptic optimal control problem with pointwise bounds on the gradient of the state variable. We derive convergence rates if the control space is ...
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Variational discretization and mixed methods for semilinear parabolic optimal control problems with integral constraint
... 2 priori error estimates. An L 2 and L ∽ priori error estimates for linear parabolic optimal control problems have been obtained when the space discretization of the state ...
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A priori error estimates for numerical methods for scalar conservation laws. Part II: flux-splitting Monotone schemes on irregular Cartesian grids
... a priori error estimates for numerical methods for scalar conservation laws by a suitable modication of Kuznetsov approximation theory ...optimal error estimates for the Engquist-Osher ...
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A priori error estimates for numerical methods for scalar conservation laws. Part II, Flux-splitting monotone schemes on irregular Cartesian grids
... truncation error due to the inconsistency introduced by the nonuni- formity of the ...of convergence of (∆x) 1/2 in L ∞ (L 1 ) can be obtained, even for inconsistent schemes, because the consistency of the ...
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A priori error estimates for higher order variational discretization and mixed finite element methods of optimal control problems
... some error estimate results for both the state, the co-state and the control approximation with convergence order h k+1 ...The priori error ...
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A priori error estimates for numerical methods for scalar conservation laws - Part III: Multidimensional flux-splitting monotone schemes on non-Cartesian grids
... 5. Concluding remarks. In [6], a general theory of a priori estimates for scalar conservation laws was proposed. The approach is based on a modification of the original Kuznetsov approximation theory [17]. ...
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A priori error estimates for numerical methods for scalar conservation laws. Part III: multidimensional flux-splitting Monotone schemes on non-Cartesian grids
... In the present paper, we generalize this result to general grids. It should be emphasized that, to the authors' knowledge, this is the rst derivation of optimal orders of convergence for truly multidimensional ...
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A unified theory of cone metric spaces and its applications to the fixed point theory
... In Section , we study cone metric spaces over solid vector spaces. The theory of such cone metric spaces is very close to the theory of the usual metric spaces. For example, every cone metric space over a solid vector ...
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Numerical analysis of a relaxed variational model of hysteresis in two phase solids
... and convergence of its discrete ...a priori stress error estimates can be ...stress error estimate of Section 5, we suggest an adaptive algorithm for automatic ...
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Heuristic constraints enforcement for training of and rule extraction from a fuzzy/neural architecture - Part II: Implementation and application
... a priori information are closed convex sets, the point of convergence of successive projections onto these sets is an element in the intersection of the constraint ...
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Convergence estimates for solution of integral equations with GMRES
... Our estimates are intended to explain the observations that the performance of GMRES is independent of the discretization if the resolution of the discretization is suciently ...r-superlinear convergence of ...
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Some Priori Estimates about Solutions to Nonhomogeneous A Harmonic Equations
... We deal with the nonhomogeneous A-harmonic equation d ∗ Ax, g du d ∗ h and the related conjugate A-harmonic equation Ax, g du h d ∗ v. Some priori estimates about solutions to these equations are obtained, ...
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On Shepard–Gupta type operators
... approximation estimates not possible by polynomials and corresponding to several nodes meshes distributions can be found for ex- ample in [1, 2, 4–7, 13, ...
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Analysis and application of the discontinuous Galerkin method to the RLW equation
... theoretical estimates; in other words, this technique produces an optimal order of convergence O(h p ...both estimates in Theorem confirm the well-know attribute of DG schemes from the class of ...
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An Explicit, Stable, High-Order Spectral Method for the Wave Equation Based on Block Gaussian Quadrature
... Table 3 lists the relative errors for various time steps and grid sizes. The errors are obtained by comparing the approximate solution to the known exact solution in the 2-norm sense. While the performance of both ...
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CAVEAT ON THE ERROR ANALYSIS FOR STEREOLOGICAL ESTIMATES
... total error of a stereological estimate arises from individual difference ...stereological error). Statistical methods for error analysis familiar to most biological researchers are based on ...
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Explicit Error Estimate for the Nonconforming Crouzeix-Raviart Finite Element
... explicit error estimate for the nonconforming Crouzeix-Raviart element for the Poisson ...explicit error bounds for the Crouzeix-Raviart element by the standard nonconforming finite element method in stead ...
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Analysis of a quasicontinuum method in one dimension
... Abstract. The quasicontinuum method is a coarse-graining technique for reducing the complexity of atomistic simulations in a static and quasistatic setting. In this paper we aim to give a detailed a priori and a ...
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Sharp uniform convergence rate of the supercell approximation of a crystalline defect
... approximation error estimate for crystal defect equilibration in the maximum norm for the strains in dimension greater than one (see [OS08, DLO10] for examples of results in one dimension and [LM13] for a result ...
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