共查询到20条相似文献,搜索用时 15 毫秒
1.
This paper proposes a mortar finite element method for solvingthe two-dimensional second-order elliptic problem with jumpsin coefficients across the interface between two subregions.Non-matching finite element grids are allowed on the interface,so independent triangulations can be used in different subregions.Explicitly realizable mortar conditions are introduced to couplethe individual discretizations. The same optimal L2-norm andenergy-norm error estimates as for regular problems are achievedwhen the interface is of arbitrary shape but smooth, thoughthe regularity of the true solution is low in the whole physicaldomain. 相似文献
2.
Cautr'es Rene; Herbin Rapha'ele; Hubert Florence 《IMA Journal of Numerical Analysis》2004,24(3):465-490
A finite volume scheme for convection diffusion equations onnon-matching grids is presented. Sharp error estimates for H2solutions of the continuous problem are obtained. A finite volumeversion of an adaptation of the Schwarz algorithm due to P.L. Lions is then studied. For a fixed mesh, its convergencetowards the finite volume scheme on the whole domain is proven.Numerical experiments are performed to illustrate the theoreticalrate of convergence of the finite volume sequences of solutionsas the mesh is refined, together with the speed of convergenceof the Schwarz algorithm. 相似文献
3.
A sequence of increasingly refined interpolation grids insidethe tetrahedron is proposed with the goal of achieving uniformconvergence and ensuring high interpolation accuracy. The numberof interpolation nodes, N, corresponds to the number of termsin the complete mth-order polynomial expansion with respectto the three tetrahedral barycentric coordinates. The proposedgrid is constructed by deploying Lobatto interpolation nodesover the faces of the tetrahedron, and then computing interiornodes using a simple formula that involves the zeros of theLobatto polynomials. Numerical computations show that the Lebesgueconstant and interpolation accuracy of the proposed grid comparefavourably with those of alternative grids constructed by solvingoptimization problems. The condition number of the mass matrixis significantly lower than that of the uniform grid and comparableto that of optimal grids proposed by previous authors. 相似文献
4.
In this paper, we present two different types of error boundsfor the approximation of functions by extrapolation methods(also called elimination methods). First, we give some a prioritype bounds; by means of these, one can, before starting theextrapolation process, estimate the errors of the extrapolatedvalues. Next, we present the so-called stopping rules; thesecan be used to decide during the process if the desired accuracyhas already been reached. Using the same techniques as for deducingthe error bounds, we then give criteria which help to predictthe form of the resulting error curves. It turns out that theseare in many cases monotone functions. Finally, two numericalexamples illustrate the results of this paper. 相似文献
5.
In this paper we derive an a posteriori error bound for the Lagrange-Galerkin discretisation of an unsteady (linear) convection-diffusion problem, assuming only that the underlying space-time mesh is nondegenerate. The proof of this error bound is based on strong stability estimates of an associated dual problem, together with the Galerkin orthogonality of the finite element method. Based on this a posteriori bound, we design and implement the corresponding adaptive algorithm to ensure global control of the error with respect to a user-defined tolerance.
6.
Error Analysis of the Enthalpy Method for the Stefan Problem 总被引:2,自引:0,他引:2
In this paper an error bound is derived for a practical piecewiselinear finite-element approximation of an enthalpy formulationof the multidimensional Stefan problem with an implicit timediscretization. It is shown that if the time step t is O(h),then the error in the temperature measured in the L2 norm isO(h). 相似文献
7.
The dependence relationships connecting equal interval splinesand their derivatives are analysed to obtain the form of theerror term when the spline is replaced by a general function.The defining equations for periodic splines of odd order ona uniform mesh are then expressed in terms of a positive definitecirculant matrix A and attainable bounds determined for thecondition number of A and for the norm of A-1. In conjunctionwith the error term associated with the dependence relationships,this enables explicit error bounds to be established for thederivatives at the knots of the spline function. Some subsidiary results in the paper also relate to B-splineson a uniform mesh. 相似文献
8.
A new a posteriori L2 norm error estimator is proposed for thePoisson equation. The error estimator can be applied to anisotropictetrahedral or triangular finite element meshes. The estimatoris rigorously analysed for Dirichlet and Neumann boundary conditions. The lower error bound relies on specifically designed anisotropicbubble functions and the corresponding inverse inequalities.The upper error bound utilizes non-standard anisotropic interpolationestimates. Its proof requires H2 regularity of the Poisson problem,and its quality depends on how good the anisotropic mesh resolvesthe anisotropy of the problem. This is measured by a so-calledmatching function. A numerical example supports the anisotropic error analysis. 相似文献
9.
Nochetto Ricardo H.; Veeser Andreas; Verani Marco 《IMA Journal of Numerical Analysis》2009,29(1):126-140
10.
Kunibert G. Siebert 《Numerische Mathematik》1996,73(3):373-398
Summary.
Besides an algorithm for local refinement, an a posteriori error
estimator is the basic tool of every adaptive finite element
method. Using information generated by such an error estimator the
refinement of the grid is controlled. For 2nd order elliptic
problems we present an error estimator for anisotropically refined
grids, like -d cuboidal and 3-d prismatic grids, that gives
correct information about the size of the error; additionally it
generates information about the direction into which some element
has to be refined to reduce the error in a proper way. Numerical
examples are presented for 2-d rectangular and 3-d prismatic grids.
Received March 15, 1994 / Revised version received June 3, 1994 相似文献
11.
In this paper, we give error expressions for the subtractionof the singularity method, the method of symmetric pairing anda method of L. M. Delves in the evaluation of the PrincipalValue of the improper integral
The error form for the subtraction of the singularity methodis used to deduce the important property that the numericalmethod for the value of the improper integral remains stableas the value of x approaches either of the end-point valuesa and b. 相似文献
12.
In this paper we propose a fully discrete finite-element schemeto solve a non-linear system of parabolic equations for a phasefield model and demonstrate an error estimate of optimal orderin L2 for this scheme. This error estimate conforms with thenumerical results presented at the end of this paper. 相似文献
13.
The paper deals with a singularly perturbed reaction diffusionmodel problem. The focus is on reliable a posteriori error estimatorsfor the H1 seminorm that can be applied to anisotropic finiteelement meshes. A residual error estimator and a local problemerror estimator are proposed and rigorously analysed. They arelocally equivalent, and both bound the error reliably. Threemodifications of these estimators are introduced and discussed. Much attention is given to the performance of the error estimatorin numerical experiments. This helps to identify those estimatorsthat are suitable for practical applications. 相似文献
14.
Anisotropic interpolation and quasi-Wilson element for narrow quadrilateral meshes 总被引:68,自引:0,他引:68
In this paper an anisotropic interpolation theorem is presentedthat can be easily used to check the anisotropy of an element.A kind of quasi-Wilson element is considered for second-orderproblems on narrow quadrilateral meshes for which the usualregularity condition K/hK c0 > 0 is not satisfied, wherehK is the diameter of the element K and K is the radius of thelargest inscribed circle in K. Anisotropic error estimates ofthe interpolation error and the consistency error in the energynorm and the L2-norm are given. Furthermore, we give a Poincaréinequality on a trapezoid which improves a result of eniek. 相似文献
15.
The author's recently introduced relative error measure forvectors is applied to the error analysis of algorithms whichproceed by successive transformation of a matrix. Instead ofmodelling the roundoff errors at each stage by A: = T(A)+E onemodels them by A: =eE T(A) where E is a small linear transformation.This can simplify analyses considerably. Applications to theparallel Jacobi method for eigenvalues, and to Gaussian elimination,are given. 相似文献
16.
The symmetric coupling of mixed finite element and boundaryelement methods is analysed for a model interface problem withthe Laplacian. The coupling involves a further continuous ansatzfunction on the interface to link the discontinuous displacementfield to the necessarily continuous boundary ansatz function.Quasi-optimal a priori error estimates and sharp a posteriorierror estimates are established which justify adaptive mesh-refiningalgorithms. Numerical experiments prove the adaptive couplingas an efficient tool for the numerical treatment of transmissionproblems. 相似文献
17.
18.
Earlier work in variational methods in the plane is extendedto N dimensions. Smoothness theorems are constructed and usedot convert means convergence to uniform convergence, establishingpointwise error bounds. A constrained variational method isused so that a priori bounds for the derivatives of the solutionmay be imposed on the approximating functions. In the non-linearproblem of compressible flow such a bound is provided by anassumption that the solution is subsonic. 相似文献
19.
In this paper, we consider the problem of selecting p pointsfrom m points, so that the p points are maximally dispersedwith respect to a specified metric. Two heuristics are studiedin terms of worst-case analysis, and a mathematical programmeis given, whose objective function is concave, together withan algorithm and error bounds on the loss of optimality arisingfrom early termination. 相似文献
20.
Dick Josef; Leobacher Gunther; Pillichshammer Friedrich 《IMA Journal of Numerical Analysis》2007,27(4):655-674