A finite element method and stabilization method for a non‐linear tricomi problem | Zendy

Lar'kin N. A. | Zendy; Schneider M. | Zendy

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A finite element method and stabilization method for a non‐linear tricomi problem

Author(s) -

Lar'kin N. A.,

Schneider M.

Publication year - 1994

Publication title -

mathematical methods in the applied sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.719

H-Index - 65

eISSN - 1099-1476

pISSN - 0170-4214

DOI - 10.1002/mma.1670170903

Subject(s) - mathematics , operator (biology) , mathematical analysis , boundary value problem , finite element method , galerkin method , linear map , order (exchange) , partial differential equation , initial value problem , cylinder , pure mathematics , geometry , biochemistry , chemistry , physics , finance , repressor , transcription factor , economics , gene , thermodynamics

We prove using the Faedo‐Galerkin method the existence of a generalized solution of an initial‐boundary value problem for the non‐linear evolution equation0 ⩽ Q ⩽ 2, in a cylinder Q T = Ω × (0, T), where u = yu xx + u yy is the Tricomi operator and l(u) a special differential operator of first order. We then show that the approximate generalized solution of problem (*) converges to the approximate generalized solution of the corresponding stationary boundary value problem as t → ∞.

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