The optimal rate of convergence of the p-version of the boundary element method in two dimensions

2004 ◽  
Vol 98 (3) ◽  
pp. 499-538 ◽  
Author(s):  
Benqi Guo ◽  
Nobert Heuer
Keyword(s):  
Boundary Element Method ◽  
Rate Of Convergence ◽  
Boundary Element ◽  
Two Dimensions ◽  
Optimal Rate ◽  
Optimal Rate Of Convergence ◽  
Element Method

scholarly journals The Virtual Element Method with curved edges

2019 ◽  
Vol 53 (2) ◽  
pp. 375-404 ◽  
Author(s):  
L. Beirão da Veiga ◽  
A. Russo ◽  
G. Vacca
Keyword(s):  
Rate Of Convergence ◽  
Two Dimensions ◽  
Optimal Rate ◽  
Virtual Element Method ◽  
Curved Boundary ◽  
Optimal Rate Of Convergence ◽  
Virtual Element ◽  
Curved Interface ◽  
Element Method

In this paper we initiate the investigation of Virtual Elements with curved faces. We consider the case of a fixed curved boundary in two dimensions, as it happens in the approximation of problems posed on a curved domain or with a curved interface. While an approximation of the domain with polygons leads, for degree of accuracy k≥2, to a sub-optimal rate of convergence, we show (both theoretically and numerically) that the proposed curved VEM lead to an optimal rate of convergence.

Design of Tools for Electrochemical Machining by the Boundary Element Method

1986 ◽  
Vol 200 (3) ◽  
pp. 195-205 ◽  
Author(s):  
O H Narayanan ◽  
S Hinduja ◽  
C F Noble
Keyword(s):  
Boundary Element Method ◽  
Boundary Conditions ◽  
Boundary Element ◽  
Electrochemical Machining ◽  
Two Dimensions ◽  
Different Boundary Conditions ◽  
Work Surface ◽  
Tool Profile ◽  
Tool Profiles ◽  
Element Method

Techniques for modelling electrochemical machining are briefly reviewed before concentrating on the boundary element method for computing the shape of tool profiles. The model described caters for problems which can be represented geometrically in two dimensions; it is iterative in nature and uses the approximate cos θ method to initiate the procedure. Subsequent iterations employ one of three formulations developed for correcting the tool profile to obtain workpiece equilibrium. Linear and quadratic isoparametric elements have been used and their relative accuracy is assessed. Special emphasis is placed on the design of tools expected to need sharp profile discontinuities and the merits of specifying different boundary conditions on the known work surface are examined.

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