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Identifier

uch.math.phd//1998chatzipantelidis

Title

Μελέτη μεθόδων πεπερασμένων χωρίων κια πεπερασμένων στοιχείων για προβλήματα συνοριακών και αρχικών-συνοριακών τιμών

Alternative Title

Finite volume and finite element methods for boundary and initial-boundary value problems

Author

Χατζηπαντελίδης, Παναγιώτης Ι

Abstract

We analyse numerical methods for the approximation of elliptic partial differential equations and initial and boundary value problems. In the first part we analyse new elliptic differential equations and prove finite volume discretizations of optimal order error estimates in H1, L2, L00. We show that finite volume methods are approximations of corresponding finite element methods by quadrative rules. In the second part we consider a linear parabolic problem. We discretize in space using finite volume methods and in time with the backward Euler's method. We prove optimal order error estimates. Finally consider a nonstiff initial value problem of the form Au'(t)=B(t,u), 0<=t<=t*, t*>0, where A is a linear selfadjoint and possitive definite operator in a Hilbert space and B a possibly nonlinear operator. We discretize in space using finite elemet methods and in time by multistep methods and prove optimal order error estimates. Then we apply our abstract results to specific differential equations.

Language

Greek

Subject

elliptic problems

finite elements

finite volumes

multistep methods

nonstiff initial value problems

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