Analysis of lumped approximations in the finite-element method for convection---diffusion problems

Authors:
S. V. Siryk
Affiliations:
National University of Ukraine "Kyiv Polytechnic Institute", Kyiv, Ukraine
Venue:
Cybernetics and Systems Analysis
Year:
2013

Citing 2
Cited 0

Numerical Methods for Problems with Moving Fronts

Numerical Methods for Problems with Moving Fronts
Galerkin Finite Element Methods for Parabolic Problems (Springer Series in Computational Mathematics)

Galerkin Finite Element Methods for Parabolic Problems (Springer Series in Computational Mathematics)

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Abstract

The Petrov---Galerkin finite-element method with a lumped mass matrix is analyzed. It is stated that in some cases it excessively smoothes the solutions and causes large errors. It is shown that weight functions can be chosen, which eliminate the above-mentioned drawbacks. The corresponding approximations are constructed in the form of systems of ordinary differential equations and finite-difference schemes. The theoretical results are confirmed by calculated data.