# Article

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Keywords:
numerical analysis; weak solution; boundary value problem; shallow shell; variational problem; finite elements
Summary:
The existence and the unicity of a weak solution of the boundary value problem for a shallow shell reinforced with stiffening ribs is proved by the direct variational method. The boundary value problem is solved in the space $W(\Omega)\subset H^1_0(\Omega)\times H^1_0(\Omega) \times H^2_0(\Omega)$, on which the corresponding bilinear form is coercive. A finite element method for numerical solution is introduced. The approximate solutions converge to a weak solution in the space $Q(\Omega)$.
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