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PDE’s on surfaces – a diffusive interface approach. (English) Zbl 1113.35092

A new approach to the numerical solution of PDE on surfaces is introduced. The problem is reformulated on a layer domain in one higher dimension. The convergence of the reformulated problem to original PDE is showed.

MSC:

35K55 Nonlinear parabolic equations
35K65 Degenerate parabolic equations
37E35 Flows on surfaces
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
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