Publication: Inverse inequalities on non-quasi-uniform meshes and application to the mortar element method
Inverse inequalities on non-quasi-uniform meshes and application to the mortar element method
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Dahmen, W., Faermann, B., Graham, I. G., Hackbusch, W., & Sauter, S. A. (2004). Inverse inequalities on non-quasi-uniform meshes and application to the mortar element method. Mathematics of Computation, 73(247), 1107-1138 (electronic). https://doi.org/10.1090/S0025-5718-03-01583-7
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We present a range of mesh-dependent inequalities for piecewise constant and continuous piecewise linear finite element functions u defined on locally refined shape-regular (but possibly non-quasi-uniform) meshes. These inequalities involve norms of the form ∥h α u∥ W s,p (Ω) for positive and negative s and α, where h is a function which reflects the local mesh diameter in an appropriate way. The only global parameter involved is N, the total number of degrees of freedom in the finite element space, and we avoid estimates involving ei
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- Dahmen, W
- Faermann, B
- Graham, I G
- Hackbusch, W
- Sauter, S A
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Dahmen, W., Faermann, B., Graham, I. G., Hackbusch, W., & Sauter, S. A. (2004). Inverse inequalities on non-quasi-uniform meshes and application to the mortar element method. Mathematics of Computation, 73(247), 1107-1138 (electronic). https://doi.org/10.1090/S0025-5718-03-01583-7
