Finite-difference vs finite-volume schemes for conservation laws












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As far as I know we don't use finite difference scheme for conservation law because solution of conservation law makes no sense pointwise as its only in $L^{infty}$. But however we use finite difference scheme for linear transport equation ($u_t+au_x=0$), which is a conservation law with flux $f(u)=au$.
Why is this so?
What is the difference between solutions of transport equation and conservation laws when flux is not linear?
What happens if we use finite volume schemes for transport equation?










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    1












    $begingroup$


    As far as I know we don't use finite difference scheme for conservation law because solution of conservation law makes no sense pointwise as its only in $L^{infty}$. But however we use finite difference scheme for linear transport equation ($u_t+au_x=0$), which is a conservation law with flux $f(u)=au$.
    Why is this so?
    What is the difference between solutions of transport equation and conservation laws when flux is not linear?
    What happens if we use finite volume schemes for transport equation?










    share|cite|improve this question











    $endgroup$















      1












      1








      1





      $begingroup$


      As far as I know we don't use finite difference scheme for conservation law because solution of conservation law makes no sense pointwise as its only in $L^{infty}$. But however we use finite difference scheme for linear transport equation ($u_t+au_x=0$), which is a conservation law with flux $f(u)=au$.
      Why is this so?
      What is the difference between solutions of transport equation and conservation laws when flux is not linear?
      What happens if we use finite volume schemes for transport equation?










      share|cite|improve this question











      $endgroup$




      As far as I know we don't use finite difference scheme for conservation law because solution of conservation law makes no sense pointwise as its only in $L^{infty}$. But however we use finite difference scheme for linear transport equation ($u_t+au_x=0$), which is a conservation law with flux $f(u)=au$.
      Why is this so?
      What is the difference between solutions of transport equation and conservation laws when flux is not linear?
      What happens if we use finite volume schemes for transport equation?







      pde numerical-methods hyperbolic-equations transport-equation






      share|cite|improve this question















      share|cite|improve this question













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      edited Jan 10 at 9:07









      Harry49

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      6,18331132










      asked Jan 9 at 17:20









      RosyRosy

      1095




      1095






















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