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In this work we prove a weak Noether type theorem for a class of variational problems which include broken extremals. We then use this result to prove discrete Noether type conservation laws for certain classes of finite element discretisation of a model elliptic problem. In addition we study how well the finite element scheme satisfies the continuous conservation laws arising from the application of Noethers 1st Theorem (E. Noether 1918). We summarise extensive numerical tests, illustrating the conservativity of the discrete Noether law using the $p$--Laplacian as an example.
Stokes variational inequalities arise in the formulation of glaciological problems involving contact. Two important examples of such problems are that of the grounding line of a marine ice sheet and the evolution of a subglacial cavity. In general, r
We study the regularity of the solution to an obstacle problem for a class of integro-differential operators. The differential part is a second order elliptic operator, whereas the nonlocal part is given by the integral fractional Laplacian. The obta
Fourth-order differential equations play an important role in many applications in science and engineering. In this paper, we present a three-field mixed finite-element formulation for fourth-order problems, with a focus on the effective treatment of
We extend our analysis on the Oldroyd-B model in Barrett and Boyaval [1] to consider the finite element approximation of the FENE-P system of equations, which models a dilute polymeric fluid, in a bounded domain $D $subset$ R d , d = 2 or 3$, subject
The aim of this paper is the numerical study of a class of nonlinear nonlocal degenerate parabolic equations. The convergence and error bounds of the solutions are proved for a linearized Crank-Nicolson-Galerkin finite element method with polynomial