A weak discrete maximum principle and stability of the finite element method in on plane polygonal domains. I
Author:
Alfred H. Schatz
Journal:
Math. Comp. 34 (1980), 7791
MSC:
Primary 65N30
MathSciNet review:
551291
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Abstract: Let be a polygonal domain in the plane and denote the finite element space of continuous piecewise polynomials of degree defined on a quasiuniform triangulation of (with triangles roughly of size h). It is shown that if is a "discrete harmonic function" then an a priori estimate (a weak maximum principle) of the form holds. Now let u be a continuous function on and be the usual finite element projection of u into (with interpolating u at the boundary nodes). It is shown that for any This says that (modulo a logarithm for ) the finite element method is bounded in on plane polygonal domains.
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DOI:
http://dx.doi.org/10.1090/S00255718198005512913
PII:
S 00255718(1980)05512913
Article copyright:
© Copyright 1980
American Mathematical Society
