A rate of convergence bound of regular-grid difference schemes for elliptical equations with discontinuous coefficients

1992 ◽  
Vol 58 (1) ◽  
pp. 17-21
Author(s):  
S. A. Voitsekhovskii ◽  
V. L. Makarov
Keyword(s):  
Rate Of Convergence ◽  
Discontinuous Coefficients ◽  
Difference Schemes ◽  
Regular Grid ◽  
Convergence Bound

Rate of convergence bound of difference schemes for the first boundary-value problem of elasticity theory in arbitrary domains

1993 ◽  
Vol 66 (3) ◽  
pp. 2272-2279
Author(s):  
S. A. Voitsekhovskii ◽  
V. M. Kalinin ◽  
V. L. Makarov
Keyword(s):  
Boundary Value Problem ◽  
Rate Of Convergence ◽  
Elasticity Theory ◽  
Boundary Value ◽  
Difference Schemes ◽  
Convergence Bound

Rate of convergence bound of difference schemes for quasilinear elliptical equations with solutions inW 2 1

1994 ◽  
Vol 72 (3) ◽  
pp. 3086-3090
Author(s):  
T. G. Voitsekhovskaya
Keyword(s):  
Rate Of Convergence ◽  
Difference Schemes ◽  
Convergence Bound

The Rate of Convergence of Some Difference Schemes

1968 ◽  
Vol 5 (2) ◽  
pp. 363-406 ◽  
Author(s):  
G. W. Hedstrom
Keyword(s):  
Rate Of Convergence ◽  
Difference Schemes

On Finite Difference Schemes for Elliptic Equations with Discontinuous Coefficients

2013 ◽  
Vol 13 (3) ◽  
pp. 281-289
Author(s):  
Manfred Dobrowolski
Keyword(s):  
Finite Element ◽  
Finite Difference ◽  
Elliptic Equations ◽  
Approximation Error ◽  
Discontinuous Coefficients ◽  
Difference Schemes ◽  
Finite Difference Schemes ◽  
The Finite Element Method ◽  
Order Four ◽  
Element Theory

Abstract. We study the convergence of finite difference schemes for approximating elliptic equations of second order with discontinuous coefficients. Two of these finite difference schemes arise from the discretization by the finite element method using bilinear shape functions. We prove an convergence for the gradient, if the solution is locally in H3. Thus, in contrast to the first order convergence for the gradient obtained by the finite element theory we show that the gradient is superclose. From the Bramble–Hilbert Lemma we derive a higher order compact (HOC) difference scheme that gives an approximation error of order four for the gradient. A numerical example is given.

scholarly journals On the Rate of Convergence of Difference Schemes for the Poisson Equation with Dynamic Interface Conditions

2003 ◽  
Vol 3 (1) ◽  
pp. 177-188 ◽  
Author(s):  
Boško Jovanovič ◽  
Lubin G. Vulkov
Keyword(s):  
Rate Of Convergence ◽  
Difference Schemes ◽  
Interface Condition ◽  
Problem Solution ◽  
Two Dimensional ◽  
Differential Problem ◽  
Logarithmic Factor ◽  
The Poisson Equation ◽  
Dynamic Interface ◽  
Sobolev Norms

AbstractThe convergence of difference schemes for the two–dimensional weakly parabolic equation (elliptic equation with a dynamic interface condition) is studied. Estimates for the rate of convergence “almost” (except for the logarithmic factor) compatible with the smoothness of the differential problem solution in special discrete Sobolev norms are obtained.

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