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Numerische Mathematik

, Volume 58, Issue 1, pp 95–108 | Cite as

A finite element method for the nonlinear Tricomi problem

  • A. K. Aziz
  • R. Lemmert
  • M. Schneider
Article

Summary

We consider a finite element procedure for numerical solution of the nonlinear problem:L[u]=yu xx +u yy +r(x,y)u=f(x, y, u) in a simply connected regionG in thex-y plane. The boundary ofG consists of Γ0, Γ1, and Γ2 and we impose the boundary condition\(u|_{\Gamma _0 \cup \Gamma _1 } = 0\). Γ0 is assumed to be a piecewises smooth curve lying in the half-planey>0 with endpointsA(−1, 0) andB(0, 0). Γ1 and Γ2 are characteristics of the operatorL issued fromA andB which intersect at the pointC(−1/2,yc). An error analysis of the method is also given.

Subject classification

AMS(MOS) 65N30 [CR: G1.8] 

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Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • A. K. Aziz
    • 1
  • R. Lemmert
    • 2
  • M. Schneider
    • 2
  1. 1.Department of MathematicsUniversity of MarylandBaltimoreUSA
  2. 2.Department of MathematicsUniversity of KarlsruheKarlsruheGermany

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