Abstract
This paper provides a discrete Poincaré inequality in n space
dimensions on a simplex K with explicit constants. This inequality bounds the norm of the piecewise derivative of
functions with integral mean zero on K and all integrals of jumps zero
along all interior sides by its Lebesgue norm times
Funding source: Deutsche Forschungsgemeinschaft
Award Identifier / Grant number: CA 151/22-1
Funding statement: The authors acknowledge support of the Deutsche Forschungsgemeinschaft in the Priority Program 1748 “Reliable simulation techniques in solid mechanics. Development of non-standard discretization methods, mechanical and mathematical analysis” under the project “Foundation and application of generalized mixed FEM towards nonlinear problems in solid mechanics”. Parts of the manuscript have been finalized while the first author enjoyed the fruitful atmosphere of the IHP quarter on Numerical Methods for PDEs in Paris; the support through the program is thankfully acknowledged. The second author is supported by the Berlin Mathematical School.
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