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Paul
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Are additional penalty methodsterms necessary to solve elliptic PDE's with DG-FEM?

After a cursory glance at several references to discontinuous galerkin finite element methods for the elliptic poisson PDE, i notice that all of them emphasize using penalty methods where an additional term in the weak form (involving the average and jump operators of the test function and trial functions) is penalized.

My colleagues seem to indicate that this termis the way it is usually done, but can't really explain why. For hyperbolic PDE's involving conservation laws, no such additional penalty term is needed. So, i'm rather curiousi wonder if they are absolutely necessary. And if so, why? That

That is, what exactly goes wrong if i use DG-FEM for the poisson problem and omit the penalty term? Does the method lose coercivity or boundedness, for example? How does the penalty term fix this problem?

Are penalty methods necessary to solve elliptic PDE's with DG-FEM?

After a cursory glance at several references to discontinuous galerkin finite element methods for the elliptic poisson PDE, i notice that all of them emphasize using penalty methods where an additional term in the weak form (involving the average and jump operators of the test function and trial functions) is penalized.

My colleagues seem to indicate that this term is usually done, can't really explain why. For hyperbolic PDE's involving conservation laws, no such additional term is needed. So, i'm rather curious if they are absolutely necessary. And if so, why? That is, what exactly goes wrong if i use DG-FEM for the poisson problem and omit the penalty term? Does the method lose coercivity or boundedness, for example? How does the penalty term fix this problem?

Are additional penalty terms necessary to solve elliptic PDE's with DG-FEM?

After a cursory glance at several references to discontinuous galerkin finite element methods for the elliptic poisson PDE, i notice that all of them emphasize using penalty methods where an additional term in the weak form (involving the average and jump operators of the test function and trial functions) is penalized.

My colleagues seem to indicate that this is the way it is usually done, but can't really explain why. For hyperbolic PDE's involving conservation laws, no such additional penalty term is needed. So, i wonder if they are absolutely necessary. And if so, why?

That is, what exactly goes wrong if i use DG-FEM for the poisson problem and omit the penalty term? Does the method lose coercivity or boundedness, for example? How does the penalty term fix this problem?

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Paul
Paul
  • 12.2k
  • 8
  • 59
  • 132

Are penalty methods necessaynecessary to solve elliptic PDE's with DG-FEM?

Source Link
Paul
Paul
  • 12.2k
  • 8
  • 59
  • 132

Are penalty methods necessay to solve elliptic PDE's with DG-FEM?

After a cursory glance at several references to discontinuous galerkin finite element methods for the elliptic poisson PDE, i notice that all of them emphasize using penalty methods where an additional term in the weak form (involving the average and jump operators of the test function and trial functions) is penalized.

My colleagues seem to indicate that this term is usually done, can't really explain why. For hyperbolic PDE's involving conservation laws, no such additional term is needed. So, i'm rather curious if they are absolutely necessary. And if so, why? That is, what exactly goes wrong if i use DG-FEM for the poisson problem and omit the penalty term? Does the method lose coercivity or boundedness, for example? How does the penalty term fix this problem?