tailieunhanh - FEM for Elliptic problems

FEM for Elliptic problems presented Introduction; variational formulation; existence of solutions: lax-milgram theorem; FEM problem,. Invite you to consult the documentation | FEM for Elliptic Problems Sebastian Gonzalez Pintor November, 2016 Proof. Multiply equation (D) by v ∈ V and integrate over the whole domain Z 1 Z 1 00 f v dx, u v dx = − We follow the results from [Joh12] and [And15]. 1 Introduction then we integrate by parts and use the boundary conditions on the left side to obtain Z 1 Z 1 − u00 v dx = − [u0 v]10 + u0 v 0 dx Outline: Variational form. and Minimization prob. • • • • 0 0 Definition of (D), (V) and (M) Equivalence (D) ⇒ (V ) ⇔ (M ) If u ∈ C 2 then (D) ⇐ (V ) Uniqueness of (V ). 0 0 = −u0 (1)v(1) + u0 (0)v(0) +(u0 , v 0 ) {z }

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